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Аналитическое решение этого уравнения можно получить в Maple </f> </inlineAttr> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">(файл: "РешДУ_В_Maple_Упражнение.mws")</inlineAttr> </f> </text> </region> <region region-id="179" left="24" top="144.75" width="487.5" height="57" align-x="24" align-y="156" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Ниже запишем алгоритм решения этого уравнения по методу "стрельбы", исходя</f> <f family="Arial Cyr" charset="204" size="12">из структуры общего решения: </f> <region region-id="426" left="192" top="159" width="114" height="15.75" align-x="219.75" align-y="170.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:id xml:space="preserve">y0</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">B</ml:id> <ml:apply> <ml:id xml:space="preserve">y1</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="6"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">, где у0(х) - частное решение не-</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">однородного </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12">уравнения</f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">, у1(х) - общее решение однородного уравнения.</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12">Дано:</f> </text> </region> <region region-id="500" left="30" top="211.5" width="50.25" height="21" align-x="59.25" align-y="228" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">p</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">x</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="7"/> </region> <region region-id="501" left="108" top="211.5" width="55.5" height="21" align-x="134.25" 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charset="204" size="12">х</f> <f family="Arial Cyr" charset="204" size="12">0+</f> <f family="Arial Cyr" charset="204" size="12"> j </f> <f family="Arial Cyr" charset="204" size="12">*</f> <f family="Arial Cyr" charset="204" size="12"> h </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-style="normal">(равенство приблизительное).</inlineAttr> </f> </text> </region> <region region-id="524" left="186" top="354.75" width="30.75" height="15.75" align-x="200.25" align-y="366" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">b</ml:id> <ml:real>4</ml:real> </ml:define> </math> <rendering item-idref="16"/> </region> <region region-id="525" left="246" top="346.5" width="91.5" height="33.75" align-x="258.75" align-y="366" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">J</ml:id> <ml:apply> <ml:id xml:space="preserve">floor</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">b</ml:id> <ml:id xml:space="preserve">x0</ml:id> </ml:apply> <ml:id xml:space="preserve">h</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="17"/> </region> <region region-id="536" left="372" top="354.75" width="39.75" height="15.75" align-x="384" align-y="366" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">J</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>20</ml:real> </result> </ml:eval> </math> <rendering item-idref="18"/> </region> <region region-id="182" left="24" top="396.75" width="210" height="13.5" align-x="24" align-y="408" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Перейдем к дискретным переменным:</f> </text> </region> <region region-id="526" left="270" top="396.75" width="45" height="15.75" align-x="284.25" align-y="408" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">k</ml:id> <ml:range> <ml:real>0</ml:real> <ml:id xml:space="preserve">J</ml:id> </ml:range> </ml:define> </math> <rendering item-idref="19"/> </region> <region region-id="527" left="348" top="396.75" width="69" height="17.25" align-x="366.75" align-y="408" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">x0</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">k</ml:id> <ml:id xml:space="preserve">h</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="20"/> </region> <region region-id="571" left="132" top="432.75" width="42.75" height="17.25" align-x="153" align-y="444" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">N</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>2</ml:real> </result> </ml:eval> </math> <rendering item-idref="21"/> </region> <region region-id="572" left="204" top="432.75" width="39" height="17.25" align-x="225" align-y="444" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">N</ml:id> </ml:apply> <ml:id xml:space="preserve">gr</ml:id> </ml:apply> </math> <rendering item-idref="22"/> </region> <region region-id="535" left="288" top="432.75" width="39" height="17.25" align-x="305.25" align-y="444" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>4</ml:real> </result> </ml:eval> </math> <rendering item-idref="23"/> </region> <region region-id="557" left="360" top="432.75" width="32.25" height="17.25" align-x="377.25" align-y="444" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> <ml:id xml:space="preserve">b</ml:id> </ml:apply> </math> <rendering item-idref="24"/> </region> <region region-id="368" left="24" top="462.75" width="193.5" height="13.5" align-x="24" align-y="474" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Левое граничное условие:<sp count="2"/>если</f> </text> </region> <region region-id="425" left="240" top="462.75" width="45.75" height="17.25" align-x="264.75" align-y="474" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y0</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:id xml:space="preserve" font="1">s1</ml:id> </ml:define> </math> <rendering item-idref="25"/> </region> <region region-id="556" left="24" top="498.75" width="104.25" height="13.5" align-x="24" align-y="510" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">то<sp count="2"/>из уравнения: </f> </text> </region> <region region-id="555" left="162" top="498.75" width="114" height="15.75" align-x="189.75" align-y="510" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:id xml:space="preserve">y0</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">B</ml:id> <ml:apply> <ml:id xml:space="preserve">y1</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="26"/> </region> <region region-id="554" left="312" top="498.75" width="42.75" height="13.5" align-x="312" align-y="510" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">следует</f> </text> </region> <region region-id="553" left="390" top="498.75" width="41.25" height="17.25" align-x="414.75" align-y="510" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y1</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:real>0</ml:real> </ml:define> </math> <rendering item-idref="27"/> </region> <region region-id="184" left="24" top="528" width="491.25" height="49.5" align-x="24" align-y="540" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Здесь и далее введены обозначения: </f> <region region-id="97" left="233.25" top="528.75" width="15" height="17.25" align-x="240" align-y="540" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:indexer/> <ml:id xml:space="preserve">y0</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </math> <rendering item-idref="28"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> - дискретные значения частного решения неоднородного дифференциального<sp count="2"/>уравнения;<sp count="2"/> </inlineAttr> </f> <region region-id="98" left="297" top="546.75" width="15" height="17.25" align-x="303.75" align-y="558" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:indexer/> <ml:id xml:space="preserve">y1</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </math> <rendering item-idref="29"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> - </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12">дискретные значения общего решения однородного </f> <f family="Arial Cyr" charset="204" size="12">дифференциального </f> <f family="Arial Cyr" charset="204" size="12"> уравнения.</f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> </text> </region> <region region-id="185" left="24" top="585.75" width="462.75" height="85.5" align-x="24" align-y="606" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Произвольно задаем: </f> <region region-id="478" left="145.5" top="594.75" width="42" height="15.75" align-x="162" align-y="606" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">m</ml:id> <ml:real>0.5</ml:real> </ml:define> </math> <rendering item-idref="30"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp count="3"/>+</inlineAttr> </f> <region region-id="610" left="204" top="586.5" width="43.5" height="33.75" align-x="231" align-y="606" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:div/> <ml:id xml:space="preserve">FRAME</ml:id> <ml:real>50</ml:real> </ml:apply> </math> <rendering item-idref="31"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp count="3"/> </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12">и решения на следующем шаге</f> <f family="Arial Cyr" charset="204" size="12"> j </f> <f family="Arial Cyr" charset="204" size="12">=1</f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <region region-id="30" left="27" top="621" width="76.5" height="33.75" align-x="51.75" align-y="640.5" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y0</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y0</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve">h</ml:id> <ml:id xml:space="preserve">m</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="32"/> </region> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12"> , </f> </inlineAttr> <region region-id="31" left="113.25" top="629.25" width="40.5" height="17.25" align-x="138" align-y="640.5" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y1</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:id xml:space="preserve">h</ml:id> </ml:define> </math> <rendering item-idref="33"/> </region> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12"> , при этом должно выполняться условие </f> </inlineAttr> <region region-id="32" left="378.75" top="629.25" width="39" height="17.25" align-x="402.75" align-y="640.5" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:notEqual/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y1</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="34"/> </region> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12"> . Этого достаточно, чтобы определить все остальные y0</f> </inlineAttr> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> j </inlineAttr> </f> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12">, y1</f> </inlineAttr> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> j </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">,<sp count="2"/>j=2,J.</inlineAttr> </f> </text> </region> <region region-id="186" left="24" top="714" width="63" height="14.25" align-x="24" align-y="726" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12"> Алгоритм: </f> </text> </region> <region region-id="128" left="108" top="714.75" width="42.75" height="15.75" align-x="120" align-y="726" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">j</ml:id> <ml:range> <ml:real>1</ml:real> <ml:id xml:space="preserve">J</ml:id> </ml:range> </ml:define> </math> <rendering item-idref="35"/> </region> <region region-id="325" left="198" top="714.75" width="54.75" height="17.25" align-x="222" align-y="726" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y0</ml:id> <ml:real>1</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>1.4</ml:real> </result> </ml:eval> </math> <rendering item-idref="36"/> </region> <region region-id="187" left="24" top="744.75" width="480.75" height="123" align-x="24" align-y="756" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Запишем рекуррентные формулы вычисления частного и общего решений соответствующего неоднородного и однородного дифференциальных уравнений, </f> <f family="Arial Cyr" charset="204" size="12">представленных в разностном виде: </f> <region region-id="122" left="225.75" top="772.5" width="200.25" height="40.5" align-x="394.5" align-y="793.5" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math20"> <originRef doc-id="6b6bb771-c8cb-4bff-860d-621d172ea4a7" version-id="e9da8135-3741-4df9-bcf9-e81e62c8b289" branch-id="00000000-0000-0000-0000-000000000000" revision-num="2" is-modified="true" region-id="122" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№2\Упражн2_1_2.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash>6349eb85eba8e44f7b1cdf082a8be8c9</hash> </originRef> <parentRef doc-id="6b6bb771-c8cb-4bff-860d-621d172ea4a7" version-id="e9da8135-3741-4df9-bcf9-e81e62c8b289" branch-id="00000000-0000-0000-0000-000000000000" revision-num="2" is-modified="true" region-id="122" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№2\Упражн2_1_2.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash>6349eb85eba8e44f7b1cdf082a8be8c9</hash> </parentRef> <comment xmlns="http://schemas.mathsoft.com/provenance10"/> <originComment xmlns="http://schemas.mathsoft.com/provenance10"/> <contentHash xmlns="http://schemas.mathsoft.com/provenance10">191b3b78404bfa0ed9ef6e5d24432299</contentHash> <ml:apply> <ml:equal/> <ml:apply> <ml:plus/> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:apply> <ml:minus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y0</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">j</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y0</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y0</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">j</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">h</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">p</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y0</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:provenance> </math> <rendering item-idref="37"> <element-image-map> <box left="1.5" top="0.75" width="198.75" height="39" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> ,<sp count="4"/> </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp count="2"/> </inlineAttr> </f> <region region-id="123" left="30" top="813.75" width="183.75" height="40.5" align-x="198.75" align-y="834.75" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math20"> <originRef doc-id="6b6bb771-c8cb-4bff-860d-621d172ea4a7" version-id="e9da8135-3741-4df9-bcf9-e81e62c8b289" branch-id="00000000-0000-0000-0000-000000000000" revision-num="2" is-modified="true" region-id="123" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№2\Упражн2_1_2.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash>6349eb85eba8e44f7b1cdf082a8be8c9</hash> </originRef> <parentRef doc-id="6b6bb771-c8cb-4bff-860d-621d172ea4a7" version-id="e9da8135-3741-4df9-bcf9-e81e62c8b289" branch-id="00000000-0000-0000-0000-000000000000" revision-num="2" is-modified="true" region-id="123" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№2\Упражн2_1_2.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash>6349eb85eba8e44f7b1cdf082a8be8c9</hash> </parentRef> <comment xmlns="http://schemas.mathsoft.com/provenance10"/> <originComment xmlns="http://schemas.mathsoft.com/provenance10"/> <contentHash xmlns="http://schemas.mathsoft.com/provenance10">3c1c6e6b820d7d0fdb3a862a82e6b8aa</contentHash> <ml:apply> <ml:equal/> <ml:apply> <ml:plus/> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:apply> <ml:minus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y1</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">j</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y1</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y1</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">j</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">h</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">p</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y1</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:real>0</ml:real> </ml:apply> </ml:provenance> </math> <rendering item-idref="38"> <element-image-map> <box left="1.5" top="0.75" width="182.25" height="39" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <f family="Arial Cyr" charset="204" size="12">Выразим из этих уравнений :</f> </text> </region> <region region-id="413" left="36" top="883.5" width="223.5" height="22.5" align-x="69.75" align-y="900" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y0</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">j</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">h</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">p</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y0</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y0</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">j</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y0</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="39"/> </region> <region region-id="414" left="300" top="883.5" width="184.5" height="22.5" align-x="333.75" align-y="900" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y1</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">j</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">h</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y1</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">p</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y1</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">j</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y1</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="40"/> </region> <region region-id="339" left="42" top="936" width="123" height="14.25" align-x="42" align-y="948" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12">На </f> <f family="Arial Cyr" charset="204" size="12"> N </f> <f family="Arial Cyr" charset="204" size="12">-м шаге<sp count="2"/>находим:</f> </text> </region> <region region-id="601" left="348" top="927" width="72" height="36.75" align-x="363.75" align-y="948" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">B</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve" font="1">s2</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y0</ml:id> <ml:id xml:space="preserve">N</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y1</ml:id> <ml:id xml:space="preserve">N</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="41"/> </region> <region region-id="342" left="42" top="972.75" width="346.5" height="13.5" align-x="42" align-y="984" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12">Теперь выпишем все значения компонент вектора решения "y":</f> </text> </region> <region region-id="43" left="66" top="1002.75" width="45" height="15.75" align-x="80.25" align-y="1014" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">k</ml:id> <ml:range> <ml:real>0</ml:real> <ml:id xml:space="preserve">J</ml:id> </ml:range> </ml:define> </math> <rendering item-idref="42"/> </region> <region region-id="44" left="144" top="1002.75" width="87" height="17.25" align-x="162.75" align-y="1014" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y0</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">B</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y1</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="43"/> </region> <region region-id="574" left="36" top="1038.75" width="57" height="13.5" align-x="36" align-y="1050" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12">Проверка:</f> </text> </region> <region region-id="590" left="114" top="1038.75" width="40.5" height="15.75" align-x="132.75" align-y="1050" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">x0</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0</ml:real> </result> </ml:eval> </math> <rendering item-idref="44"/> </region> <region region-id="591" left="174" top="1038.75" width="39.75" height="17.25" align-x="192" align-y="1050" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y</ml:id> <ml:real>0</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>1</ml:real> </result> </ml:eval> </math> <rendering item-idref="45"/> </region> <region region-id="592" left="234" top="1038.75" width="37.5" height="17.25" align-x="252" align-y="1050" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:id xml:space="preserve">s1</ml:id> </ml:apply> </math> <rendering item-idref="46"/> </region> <region region-id="598" left="318" top="1038.75" width="42.75" height="17.25" align-x="339" align-y="1050" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">N</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>2</ml:real> </result> </ml:eval> </math> <rendering item-idref="47"/> </region> <region region-id="599" left="378" top="1038.75" width="42.75" height="17.25" align-x="399" align-y="1050" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">N</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>4</ml:real> </result> </ml:eval> </math> <rendering item-idref="48"/> </region> <region region-id="600" left="432" top="1038.75" width="40.5" height="17.25" align-x="453" align-y="1050" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">N</ml:id> </ml:apply> <ml:id xml:space="preserve">s2</ml:id> </ml:apply> </math> <rendering item-idref="49"/> </region> <region region-id="606" left="36" top="1092" width="261.75" height="195.75" align-x="36" align-y="1092" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="50"/> <rendering item-idref="51"/> </region> <region region-id="562" left="354" top="1170.75" width="140.25" height="54" align-x="354" align-y="1182" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Рис. 1. </f> <f family="Arial Cyr" charset="204" size="12">Возможна анимация </f> <f family="Arial Cyr" charset="204" size="12">графика</f> <f family="Arial Cyr" charset="204" size="12"> (39 кадров).</f> <f family="Arial Cyr" charset="204" size="12">Зависит только от "h".</f> </text> </region> <region region-id="567" left="36" top="1324.5" width="106.5" height="33.75" align-x="49.5" align-y="1344" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">n</ml:id> <ml:apply> <ml:id xml:space="preserve">round</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:real>1.4</ml:real> <ml:id xml:space="preserve">x0</ml:id> </ml:apply> <ml:id xml:space="preserve">h</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="52"/> </region> <region region-id="568" left="174" top="1332.75" width="34.5" height="15.75" align-x="186.75" align-y="1344" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">n</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>7</ml:real> </result> </ml:eval> </math> <rendering item-idref="53"/> </region> <region region-id="569" left="240" top="1332.75" width="48.75" height="17.25" align-x="258" align-y="1344" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>1.4000000000000001</ml:real> </result> </ml:eval> </math> <rendering item-idref="54"/> </region> <region region-id="570" left="324" top="1332.75" width="66.75" height="17.25" align-x="342" align-y="1344" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>12.008180689427801</ml:real> </result> </ml:eval> </math> <rendering item-idref="55"/> </region> <region region-id="607" left="42" top="1410.75" width="469.5" height="81" align-x="42" align-y="1422" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">На графике рис.1 нанесена точка (1.4, 11.87), полученная при решении этого </f> <f family="Arial Cyr" charset="204" size="12">уравнения в Maple численно с помощью ШПО (</f> <f family="Arial Cyr" charset="204" size="12">файл: </f> <f family="Arial Cyr" charset="204" size="12">"РешДУ_В_Maple_Упражн1.mws"</f> <f family="Arial Cyr" charset="204" size="12">). Как видно из рисунка 1 решение, полученное</f> <f family="Arial Cyr" charset="204" size="12">по методу "Стрельбы" проходит через эту точку, что говорит о высокой точности </f> <f family="Arial Cyr" charset="204" size="12">этого метода. Здесь, к сожалению, из Maple нельзя перенести график в Mathcad. </f> <f family="Arial Cyr" charset="204" size="12">Посмотреть решения в Упражнениях 2.1.1. и 2.1.2.</f> </text> </region> <region region-id="604" left="42" top="1548" width="455.25" height="68.25" align-x="42" align-y="1560" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12"> Задание </f> <f family="Arial Cyr" charset="204" size="12">. Решить методом стрельбы дифференциальные уравнения (линейные) со следующими параметрами (а</f> <f family="Arial Cyr" charset="204" size="12">налитическое решение найти с помощью Maple - </f> <f family="Arial Cyr" charset="204" size="12">файл: "РешДУ_В_Maple_Упражнение.mws")</f> <f family="Arial Cyr" charset="204" size="12">: </f> <f family="Arial Cyr" charset="204" size="12">1) р(х)=2, f(x)=cos(x). 2) </f> <f family="Arial Cyr" charset="204" size="12">р(х)=1, f(x)=sin(k*x). 3) </f> <f family="Arial Cyr" charset="204" size="12">р(х)=3, f(x)=sin(k*x)*exp(-x).</f> <f family="Arial Cyr" charset="204" size="12">Граничные условия: y(0)=1,<sp count="2"/>y(2)=2.</f> </text> </region> </regions> <binaryContent> <item item-id="1" content-encoding="gzip">H4sIAAAAAAAA/4yNvQ6CQBCEdzlQwd/GGhMbj9InsCBWJj6CnvifEA1SWPrm5+yCvUf2GGa/ GQZExBiHSVQb3OPjcnep3PO6Oz+q0tURyZljYrVzVzu1aIHplcX2cD8VdWPtmxcFM1ym7Z9K q2r5Stz79lprtVE2w2y4ZZvj8RBn/7u/8m5dueK0zANd2RZMeUJs2Ytitlj6lAO2BtGUDdvQ 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Аналитическое решение этого уравнения можно получить в Maple </f> </inlineAttr> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">(файл: "РешДУ_В_Maple_Упражнение.mws")</inlineAttr> </f> </text> </region> <region region-id="179" left="24" top="144.75" width="487.5" height="57" align-x="24" align-y="156" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Ниже запишем алгоритм решения этого уравнения по методу "стрельбы", исходя</f> <f family="Arial Cyr" charset="204" size="12">из структуры общего решения: </f> <region region-id="426" left="192" top="159" width="114" height="15.75" align-x="219.75" align-y="170.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:id xml:space="preserve">y0</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">B</ml:id> <ml:apply> <ml:id xml:space="preserve">y1</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="6"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">, где у0(х) - частное решение не-</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">однородного </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12">уравнения</f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">, у1(х) - общее решение однородного уравнения.</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12">Дано:</f> </text> </region> <region region-id="500" left="30" top="211.5" width="50.25" height="21" align-x="59.25" align-y="228" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">p</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">x</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="7"/> </region> <region region-id="501" left="108" top="211.5" width="55.5" height="21" align-x="134.25" align-y="228" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">f</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="8"/> </region> <region region-id="502" left="192" top="216.75" width="36" height="15.75" align-x="211.5" align-y="228" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">x0</ml:id> <ml:real>0</ml:real> </ml:define> </math> <rendering item-idref="9"/> </region> <region region-id="503" left="246" top="216.75" width="33.75" height="15.75" align-x="263.25" align-y="228" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">gr</ml:id> <ml:real>2</ml:real> </ml:define> </math> <rendering item-idref="10"/> </region> <region region-id="504" left="306" top="216.75" width="35.25" height="15.75" align-x="324.75" align-y="228" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">s1</ml:id> <ml:real>1</ml:real> </ml:define> </math> <rendering item-idref="11"/> </region> <region region-id="505" left="360" top="216.75" width="35.25" height="15.75" align-x="378.75" align-y="228" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">s2</ml:id> <ml:real>4</ml:real> </ml:define> </math> <rendering item-idref="12"/> </region> <region region-id="539" left="24" top="250.5" width="94.5" height="33.75" align-x="37.5" align-y="270" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">h</ml:id> <ml:apply> <ml:minus/> <ml:real>0.2</ml:real> <ml:apply> <ml:div/> <ml:id xml:space="preserve">FRAME</ml:id> <ml:real>200</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="13"/> </region> <region region-id="541" left="174" top="250.5" width="99" height="33.75" align-x="191.25" align-y="270" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">N</ml:id> <ml:apply> <ml:id xml:space="preserve">floor</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">gr</ml:id> <ml:id xml:space="preserve">x0</ml:id> </ml:apply> <ml:id xml:space="preserve">h</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="14"/> </region> <region region-id="540" left="300" top="258.75" width="44.25" height="15.75" align-x="316.5" align-y="270" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">N</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>10</ml:real> </result> </ml:eval> </math> <rendering item-idref="15"/> </region> <region region-id="523" left="24" top="306" width="469.5" height="31.5" align-x="24" align-y="318" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12">Диапазон изменения х:<sp count="2"/>x0<x<b<sp count="2"/>и gr<b, N<J. </f> <f family="Arial Cyr" charset="204" size="12">Найдем<sp count="2"/> </f> <f family="Arial Cyr" charset="204" size="12"> j </f> <f family="Arial Cyr" charset="204" size="12">,<sp count="2"/>при котором </f> <f family="Arial Cyr" charset="204" size="12"> x </f> <f family="Arial Cyr" charset="204" size="12"> j </f> <f family="Arial Cyr" charset="204" size="12">=b</f> <f family="Arial Cyr" charset="204" size="12"> из уравнения: b=</f> <f family="Arial Cyr" charset="204" size="12">х</f> <f family="Arial Cyr" charset="204" size="12">0+</f> <f family="Arial Cyr" charset="204" size="12"> j </f> <f family="Arial Cyr" charset="204" size="12">*</f> <f family="Arial Cyr" charset="204" size="12"> h </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-style="normal">(равенство приблизительное).</inlineAttr> </f> </text> </region> <region region-id="524" left="186" top="354.75" width="30.75" height="15.75" align-x="200.25" align-y="366" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">b</ml:id> <ml:real>4</ml:real> </ml:define> </math> <rendering item-idref="16"/> </region> <region region-id="525" left="246" top="346.5" width="91.5" height="33.75" align-x="258.75" align-y="366" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">J</ml:id> <ml:apply> <ml:id xml:space="preserve">floor</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">b</ml:id> <ml:id xml:space="preserve">x0</ml:id> </ml:apply> <ml:id xml:space="preserve">h</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="17"/> </region> <region region-id="536" left="372" top="354.75" width="39.75" height="15.75" align-x="384" align-y="366" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">J</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>20</ml:real> </result> </ml:eval> </math> <rendering item-idref="18"/> </region> <region region-id="182" left="24" top="396.75" width="210" height="13.5" align-x="24" align-y="408" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Перейдем к дискретным переменным:</f> </text> </region> <region region-id="526" left="270" top="396.75" width="45" height="15.75" align-x="284.25" align-y="408" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">k</ml:id> <ml:range> <ml:real>0</ml:real> <ml:id xml:space="preserve">J</ml:id> </ml:range> </ml:define> </math> <rendering item-idref="19"/> </region> <region region-id="527" left="348" top="396.75" width="69" height="17.25" align-x="366.75" align-y="408" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">x0</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">k</ml:id> <ml:id xml:space="preserve">h</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="20"/> </region> <region region-id="571" left="132" top="432.75" width="42.75" height="17.25" align-x="153" align-y="444" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">N</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>2</ml:real> </result> </ml:eval> </math> <rendering item-idref="21"/> </region> <region region-id="572" left="204" top="432.75" width="39" height="17.25" align-x="225" align-y="444" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">N</ml:id> </ml:apply> <ml:id xml:space="preserve">gr</ml:id> </ml:apply> </math> <rendering item-idref="22"/> </region> <region region-id="535" left="288" top="432.75" width="39" height="17.25" align-x="305.25" align-y="444" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>4</ml:real> </result> </ml:eval> </math> <rendering item-idref="23"/> </region> <region region-id="557" left="360" top="432.75" width="32.25" height="17.25" align-x="377.25" align-y="444" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> <ml:id xml:space="preserve">b</ml:id> </ml:apply> </math> <rendering item-idref="24"/> </region> <region region-id="368" left="24" top="462.75" width="193.5" height="13.5" align-x="24" align-y="474" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Левое граничное условие:<sp count="2"/>если</f> </text> </region> <region region-id="425" left="240" top="462.75" width="45.75" height="17.25" align-x="264.75" align-y="474" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y0</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:id xml:space="preserve" font="1">s1</ml:id> </ml:define> </math> <rendering item-idref="25"/> </region> <region region-id="556" left="24" top="498.75" width="104.25" height="13.5" align-x="24" align-y="510" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">то<sp count="2"/>из уравнения: </f> </text> </region> <region region-id="555" left="162" top="498.75" width="114" height="15.75" align-x="189.75" align-y="510" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:id xml:space="preserve">y0</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">B</ml:id> <ml:apply> <ml:id xml:space="preserve">y1</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="26"/> </region> <region region-id="554" left="312" top="498.75" width="42.75" height="13.5" align-x="312" align-y="510" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">следует</f> </text> </region> <region region-id="553" left="390" top="498.75" width="41.25" height="17.25" align-x="414.75" align-y="510" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y1</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:real>0</ml:real> </ml:define> </math> <rendering item-idref="27"/> </region> <region region-id="184" left="24" top="528" width="491.25" height="49.5" align-x="24" align-y="540" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Здесь и далее введены обозначения: </f> <region region-id="97" left="233.25" top="528.75" width="15" height="17.25" align-x="240" align-y="540" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:indexer/> <ml:id xml:space="preserve">y0</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </math> <rendering item-idref="28"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> - дискретные значения частного решения неоднородного дифференциального<sp count="2"/>уравнения;<sp count="2"/> </inlineAttr> </f> <region region-id="98" left="297" top="546.75" width="15" height="17.25" align-x="303.75" align-y="558" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:indexer/> <ml:id xml:space="preserve">y1</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </math> <rendering item-idref="29"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> - </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12">дискретные значения общего решения однородного </f> <f family="Arial Cyr" charset="204" size="12">дифференциального </f> <f family="Arial Cyr" charset="204" size="12"> уравнения.</f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> </text> </region> <region region-id="185" left="24" top="585.75" width="462.75" height="85.5" align-x="24" align-y="606" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Произвольно задаем: </f> <region region-id="478" left="145.5" top="594.75" width="42" height="15.75" align-x="162" align-y="606" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">m</ml:id> <ml:real>0.5</ml:real> </ml:define> </math> <rendering item-idref="30"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp count="3"/>+</inlineAttr> </f> <region region-id="610" left="204" top="586.5" width="43.5" height="33.75" align-x="231" align-y="606" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:div/> <ml:id xml:space="preserve">FRAME</ml:id> <ml:real>50</ml:real> </ml:apply> </math> <rendering item-idref="31"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp count="3"/> </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12">и решения на следующем шаге</f> <f family="Arial Cyr" charset="204" size="12"> j </f> <f family="Arial Cyr" charset="204" size="12">=1</f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <region region-id="30" left="27" top="621" width="76.5" height="33.75" align-x="51.75" align-y="640.5" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y0</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y0</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve">h</ml:id> <ml:id xml:space="preserve">m</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="32"/> </region> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12"> , </f> </inlineAttr> <region region-id="31" left="113.25" top="629.25" width="40.5" height="17.25" align-x="138" align-y="640.5" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y1</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:id xml:space="preserve">h</ml:id> </ml:define> </math> <rendering item-idref="33"/> </region> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12"> , при этом должно выполняться условие </f> </inlineAttr> <region region-id="32" left="378.75" top="629.25" width="39" height="17.25" align-x="402.75" align-y="640.5" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:notEqual/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y1</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="34"/> </region> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12"> . Этого достаточно, чтобы определить все остальные y0</f> </inlineAttr> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> j </inlineAttr> </f> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12">, y1</f> </inlineAttr> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> j </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">,<sp count="2"/>j=2,J.</inlineAttr> </f> </text> </region> <region region-id="186" left="24" top="714" width="63" height="14.25" align-x="24" align-y="726" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12"> Алгоритм: </f> </text> </region> <region region-id="128" left="108" top="714.75" width="42.75" height="15.75" align-x="120" align-y="726" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">j</ml:id> <ml:range> <ml:real>1</ml:real> <ml:id xml:space="preserve">J</ml:id> </ml:range> </ml:define> </math> <rendering item-idref="35"/> </region> <region region-id="325" left="198" top="714.75" width="54.75" height="17.25" align-x="222" align-y="726" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y0</ml:id> <ml:real>1</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>1.4</ml:real> </result> </ml:eval> </math> <rendering item-idref="36"/> </region> <region region-id="187" left="24" top="744.75" width="480.75" height="123" align-x="24" align-y="756" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Запишем рекуррентные формулы вычисления частного и общего решений соответствующего неоднородного и однородного дифференциальных уравнений, </f> <f family="Arial Cyr" charset="204" size="12">представленных в разностном виде: </f> <region region-id="122" left="225.75" top="772.5" width="200.25" height="40.5" align-x="394.5" align-y="793.5" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math20"> <originRef doc-id="6b6bb771-c8cb-4bff-860d-621d172ea4a7" version-id="e9da8135-3741-4df9-bcf9-e81e62c8b289" branch-id="00000000-0000-0000-0000-000000000000" revision-num="2" is-modified="true" region-id="122" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№2\Упражн2_1_2.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash>6349eb85eba8e44f7b1cdf082a8be8c9</hash> </originRef> <parentRef doc-id="6b6bb771-c8cb-4bff-860d-621d172ea4a7" version-id="e9da8135-3741-4df9-bcf9-e81e62c8b289" branch-id="00000000-0000-0000-0000-000000000000" revision-num="2" is-modified="true" region-id="122" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№2\Упражн2_1_2.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash>6349eb85eba8e44f7b1cdf082a8be8c9</hash> </parentRef> <comment xmlns="http://schemas.mathsoft.com/provenance10"/> <originComment xmlns="http://schemas.mathsoft.com/provenance10"/> <contentHash xmlns="http://schemas.mathsoft.com/provenance10">191b3b78404bfa0ed9ef6e5d24432299</contentHash> <ml:apply> <ml:equal/> <ml:apply> <ml:plus/> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:apply> <ml:minus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y0</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">j</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y0</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y0</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">j</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">h</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">p</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y0</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:provenance> </math> <rendering item-idref="37"> <element-image-map> <box left="1.5" top="0.75" width="198.75" height="39" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> ,<sp count="4"/> </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp count="2"/> </inlineAttr> </f> <region region-id="123" left="30" top="813.75" width="183.75" height="40.5" align-x="198.75" align-y="834.75" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math20"> <originRef doc-id="6b6bb771-c8cb-4bff-860d-621d172ea4a7" version-id="e9da8135-3741-4df9-bcf9-e81e62c8b289" branch-id="00000000-0000-0000-0000-000000000000" revision-num="2" is-modified="true" region-id="123" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№2\Упражн2_1_2.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash>6349eb85eba8e44f7b1cdf082a8be8c9</hash> </originRef> <parentRef doc-id="6b6bb771-c8cb-4bff-860d-621d172ea4a7" version-id="e9da8135-3741-4df9-bcf9-e81e62c8b289" branch-id="00000000-0000-0000-0000-000000000000" revision-num="2" is-modified="true" region-id="123" href="c:\Documents and Settings\Konstantin\Мои документы\Ps_МГТУ\Лаборааторные работы по численным методам\ЛР№2\Упражн2_1_2.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash>6349eb85eba8e44f7b1cdf082a8be8c9</hash> </parentRef> <comment xmlns="http://schemas.mathsoft.com/provenance10"/> <originComment xmlns="http://schemas.mathsoft.com/provenance10"/> <contentHash xmlns="http://schemas.mathsoft.com/provenance10">3c1c6e6b820d7d0fdb3a862a82e6b8aa</contentHash> <ml:apply> <ml:equal/> <ml:apply> <ml:plus/> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:apply> <ml:minus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y1</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">j</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y1</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y1</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">j</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">h</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">p</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y1</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:real>0</ml:real> </ml:apply> </ml:provenance> </math> <rendering item-idref="38"> <element-image-map> <box left="1.5" top="0.75" width="182.25" height="39" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <f family="Arial Cyr" charset="204" size="12">Выразим из этих уравнений :</f> </text> </region> <region region-id="413" left="36" top="883.5" width="223.5" height="22.5" align-x="69.75" align-y="900" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y0</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">j</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">h</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">p</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y0</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y0</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">j</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y0</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="39"/> </region> <region region-id="414" left="300" top="883.5" width="184.5" height="22.5" align-x="333.75" align-y="900" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y1</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">j</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">h</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y1</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">p</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y1</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">j</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y1</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="40"/> </region> <region region-id="339" left="42" top="936" width="123" height="14.25" align-x="42" align-y="948" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12">На </f> <f family="Arial Cyr" charset="204" size="12"> N </f> <f family="Arial Cyr" charset="204" size="12">-м шаге<sp count="2"/>находим:</f> </text> </region> <region region-id="601" left="348" top="927" width="72" height="36.75" align-x="363.75" align-y="948" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">B</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve" font="1">s2</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y0</ml:id> <ml:id xml:space="preserve">N</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y1</ml:id> <ml:id xml:space="preserve">N</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="41"/> </region> <region region-id="342" left="42" top="972.75" width="346.5" height="13.5" align-x="42" align-y="984" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12">Теперь выпишем все значения компонент вектора решения "y":</f> </text> </region> <region region-id="43" left="66" top="1002.75" width="45" height="15.75" align-x="80.25" align-y="1014" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">k</ml:id> <ml:range> <ml:real>0</ml:real> <ml:id xml:space="preserve">J</ml:id> </ml:range> </ml:define> </math> <rendering item-idref="42"/> </region> <region region-id="44" left="144" top="1002.75" width="87" height="17.25" align-x="162.75" align-y="1014" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y0</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">B</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y1</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="43"/> </region> <region region-id="574" left="36" top="1038.75" width="57" height="13.5" align-x="36" align-y="1050" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12">Проверка:</f> </text> </region> <region region-id="590" left="114" top="1038.75" width="40.5" height="15.75" align-x="132.75" align-y="1050" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">x0</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0</ml:real> </result> </ml:eval> </math> <rendering item-idref="44"/> </region> <region region-id="591" left="174" top="1038.75" width="39.75" height="17.25" align-x="192" align-y="1050" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y</ml:id> <ml:real>0</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>1</ml:real> </result> </ml:eval> </math> <rendering item-idref="45"/> </region> <region region-id="592" left="234" top="1038.75" width="37.5" height="17.25" align-x="252" align-y="1050" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:id xml:space="preserve">s1</ml:id> </ml:apply> </math> <rendering item-idref="46"/> </region> <region region-id="598" left="318" top="1038.75" width="42.75" height="17.25" align-x="339" align-y="1050" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">N</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>2</ml:real> </result> </ml:eval> </math> <rendering item-idref="47"/> </region> <region region-id="599" left="378" top="1038.75" width="42.75" height="17.25" align-x="399" align-y="1050" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">N</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>4</ml:real> </result> </ml:eval> </math> <rendering item-idref="48"/> </region> <region region-id="600" left="432" top="1038.75" width="40.5" height="17.25" align-x="453" align-y="1050" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">N</ml:id> </ml:apply> <ml:id xml:space="preserve">s2</ml:id> </ml:apply> </math> <rendering item-idref="49"/> </region> <region region-id="606" left="36" top="1092" width="261.75" height="195.75" align-x="36" align-y="1092" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="50"/> <rendering item-idref="51"/> </region> <region region-id="562" left="354" top="1170.75" width="140.25" height="54" align-x="354" align-y="1182" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Рис. 1. </f> <f family="Arial Cyr" charset="204" size="12">Возможна анимация </f> <f family="Arial Cyr" charset="204" size="12">графика</f> <f family="Arial Cyr" charset="204" size="12"> (39 кадров).</f> <f family="Arial Cyr" charset="204" size="12">Зависит только от "h".</f> </text> </region> <region region-id="567" left="36" top="1324.5" width="106.5" height="33.75" align-x="49.5" align-y="1344" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">n</ml:id> <ml:apply> <ml:id xml:space="preserve">round</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:real>1.4</ml:real> <ml:id xml:space="preserve">x0</ml:id> </ml:apply> <ml:id xml:space="preserve">h</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="52"/> </region> <region region-id="568" left="174" top="1332.75" width="34.5" height="15.75" align-x="186.75" align-y="1344" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">n</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>7</ml:real> </result> </ml:eval> </math> <rendering item-idref="53"/> </region> <region region-id="569" left="240" top="1332.75" width="48.75" height="17.25" align-x="258" align-y="1344" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>1.4000000000000001</ml:real> </result> </ml:eval> </math> <rendering item-idref="54"/> </region> <region region-id="570" left="324" top="1332.75" width="66.75" height="17.25" align-x="342" align-y="1344" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>12.008180689427801</ml:real> </result> </ml:eval> </math> <rendering item-idref="55"/> </region> <region region-id="607" left="42" top="1410.75" width="469.5" height="81" align-x="42" align-y="1422" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">На графике рис.1 нанесена точка (1.4, 11.87), полученная при решении этого </f> <f family="Arial Cyr" charset="204" size="12">уравнения в Maple численно с помощью ШПО (</f> <f family="Arial Cyr" charset="204" size="12">файл: </f> <f family="Arial Cyr" charset="204" size="12">"РешДУ_В_Maple_Упражн1.mws"</f> <f family="Arial Cyr" charset="204" size="12">). Как видно из рисунка 1 решение, полученное</f> <f family="Arial Cyr" charset="204" size="12">по методу "Стрельбы" проходит через эту точку, что говорит о высокой точности </f> <f family="Arial Cyr" charset="204" size="12">этого метода. Здесь, к сожалению, из Maple нельзя перенести график в Mathcad. </f> <f family="Arial Cyr" charset="204" size="12">Посмотреть решения в Упражнениях 2.1.1. и 2.1.2.</f> </text> </region> <region region-id="604" left="42" top="1548" width="455.25" height="68.25" align-x="42" align-y="1560" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12"> Задание </f> <f family="Arial Cyr" charset="204" size="12">. Решить методом стрельбы дифференциальные уравнения (линейные) со следующими параметрами (а</f> <f family="Arial Cyr" charset="204" size="12">налитическое решение найти с помощью Maple - </f> <f family="Arial Cyr" charset="204" size="12">файл: "РешДУ_В_Maple_Упражнение.mws")</f> <f family="Arial Cyr" charset="204" size="12">: </f> <f family="Arial Cyr" charset="204" size="12">1) р(х)=2, f(x)=cos(x). 2) </f> <f family="Arial Cyr" charset="204" size="12">р(х)=1, f(x)=sin(k*x). 3) </f> <f family="Arial Cyr" charset="204" size="12">р(х)=3, f(x)=sin(k*x)*exp(-x).</f> <f family="Arial Cyr" charset="204" size="12">Граничные условия: y(0)=1,<sp count="2"/>y(2)=2.</f> </text> </region> </regions> <binaryContent> <item item-id="1" content-encoding="gzip">H4sIAAAAAAAA/4yNvQ6CQBCEdzlQwd/GGhMbj9InsCBWJj6CnvifEA1SWPrm5+yCvUf2GGa/ GQZExBiHSVQb3OPjcnep3PO6Oz+q0tURyZljYrVzVzu1aIHplcX2cD8VdWPtmxcFM1ym7Z9K q2r5Stz79lprtVE2w2y4ZZvj8RBn/7u/8m5dueK0zANd2RZMeUJs2Ytitlj6lAO2BtGUDdvQ 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