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6#>%$psiGf*6#%\"tG6\"6$%)operatorG%&arrowGF(\"\"!F(F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 83 "*) \317\356\361\353\345\344\355\345\345 \+ \356\362\360\340\347\350\354 \342 \342\350\344\345 \367\345\362\373 \360\345\365 \360\340\342\345\355\361\362\342, \352\356\362\356\360 \373\345 \347\340\357\350\361\340\355\373 \355\350\346\345. \315\363 \346\355\356\345 \350\347 \355\350\365 " }}{PARA 0 "" 0 "" {TEXT -1 32 "\361\353\345\344\363\345\362 \356\362\352\360\373\362\374, \361 \355\377\342 \340\357\356\361\362\360\356\364\373." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "u(0,t):=phi(t); u(L,t):=psi(t); \+ " }{TEXT -1 2 "1)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"uG6$\" \"!%\"tG,&\"\"\"F*-%$cosG6#F(!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >-%\"uG6$\"\"\"%\"tG\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "`D[1](u)(0,t):=phi(t); D[1](u)(L,t):=psi(t);`: " }{TEXT -1 2 "2 )" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "`D[1](u)(0,t):=phi(t); u(L,t):=psi(t);`: " }{TEXT -1 2 "3)" }{MPLTEXT 1 0 4 " " }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "`u(0,t):=phi(t); D[1](u)(L, t):=psi(t);`: " }{TEXT -1 17 " 4)" }{MPLTEXT 1 0 1 " \+ " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 49 "\317\360\356\342\345\344\345 \354 \361\345\354\340\355\362\350\367\345\361\352\356\345 \352\356\355 \342\345\360\362\350\360\356\342\340\355\350\345 \356\357\345\360\340 \362\356\360\340 " }{TEXT 270 1 "D" }{TEXT -1 3 " \342 " }{TEXT 271 4 "diff" }{TEXT -1 1 ":" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "uu (x,t): D[1](uu)(0,t): convert(%,diff); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%%evalG6$-%%diffG6$-%#uuG6$%#t1G%\"tGF,<#/F,\"\"!" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 41 "\316\362\354\345\362\350\354, \367 \362\356 \342 \361\362\360\363\352\362\363\360\345 \360\345\370\345 \355\350\377 \364\363\355\352\366\350\377 " }{TEXT 272 1 "z" }{TEXT -1 1 "(" }{TEXT 273 1 "x" }{TEXT -1 1 "," }{TEXT 274 1 "t" }{TEXT -1 39 ") \357\356\344\341\350\360\340\345\362\361\377 \362\340\352\350 \354 \356\341\360\340\347\356\354, \367\362\356\341\373 \343\360\340- " }}{PARA 0 "" 0 "" {TEXT -1 23 "\355\350\367\355\373\345 \363\361\353 \356\342\350\377 \360\345\370\345\355\350\377 " }{TEXT 275 1 "u" } {TEXT -1 1 "(" }{TEXT 276 1 "x" }{TEXT -1 1 "," }{TEXT 277 1 "t" } {TEXT -1 26 ") \361\356\342\357\340\344\340\353\350 \361\356 \347\355 \340\367\345\355\350\377\354\350 " }{TEXT 278 1 "z" }{TEXT -1 1 "(" } {TEXT 279 1 "x" }{TEXT -1 1 "," }{TEXT 280 1 "t" }{TEXT -1 26 ") \342 \+ \340\355\340\353\356\343\350\367\355\373\365 \362\356\367\352\340\365, \362\356" }}{PARA 0 "" 0 "" {TEXT -1 32 "\345\361\362\374 \350\365 \+ \360\340\347\355\356\361\362\374 \360\340\342\355\377\353\340\361\374 \+ \355\363\353\376." }}{PARA 0 "" 0 "" {TEXT -1 82 "\321\364\356\360\354 \350\360\363\345\354 \353\356\343\350\367\345\361\352\350\351 \341\353 \356\352 \342\373\341\356\360\340 \362\350\357\340 \343\360\340\355 \350\367\355\373\365 \363\361\353\356\342\350\351, \352\356\362\356 \360\373\345 \341\363\344\363\362 \356\357\360\345\344\345\353\377\362 \374" }}{PARA 0 "" 0 "" {TEXT -1 46 "(\347\340\344\340\367\340 \330 \362\363\360\354\340-\313\350\363\342\350\353\353\377) \361\356\341 \361\362\342\345\355\355\373\345 \347\355\340\367\345\355\350\377 " } {TEXT 281 1 "b" }{TEXT -1 1 "(" }{TEXT 282 1 "n" }{TEXT -1 24 ") \350 \+ \361\356\341\361\362\342\345\355\355\373\345 \364\363\355\352\366\350 \350 " }{TEXT 283 2 "Xn" }{TEXT -1 1 "(" }{TEXT 284 1 "x" }{TEXT -1 1 "," }{TEXT 285 1 "n" }{TEXT -1 3 "), " }}{PARA 0 "" 0 "" {TEXT -1 74 " \340 \362\340\352\346\345 \357\356\344\341\350\360\340\345\354\363\376 \342 \363\352\340\347\340\355\355\356\354 \342\373\370\345 \361\354 \373\361\353\345 \352 \343\360\340\355\350\367\355\373\354 \363\361 \353\356\342\350\377\354 \364\363\355\352\366\350\376 " }{TEXT 286 1 "z" }{TEXT -1 1 "(" }{TEXT 287 1 "x" }{TEXT -1 1 "," }{TEXT 288 1 "t" }{TEXT -1 2 "):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "if u(0,t )=phi(t)and u(L,t)=psi(t) then" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "b :=n->Pi*n/L: Xn:=(x,n)->sin(b(n)*x):" }}{PARA 0 "> " 0 "" {XPPEDIT 19 1 "z:=(x,t)->phi(t)+x/L*(psi(t)-phi(t))" "6#>%\"zGf*6$%\"xG%\"tG7\"6$% )operatorG%&arrowG6\",&-%$phiG6#F(\"\"\"*(F'F2%\"LG!\"\",&-%$psiG6#F(F 2-F06#F(F5F2F2F-F-F-" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "elif D[1](u )(0,t)=phi(t) and D[1](u)(L,t)=psi(t) then" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "b:=n->Pi*n/L: Xn:=(x,n)->cos(b(n)*x): " }}{PARA 0 "> \+ " 0 "" {XPPEDIT 19 1 "z:=(x,t)->x*phi(t)+x^2/2/L*(psi(t)-phi(t))" "6#> %\"zGf*6$%\"xG%\"tG7\"6$%)operatorG%&arrowG6\",&*&F'\"\"\"-%$phiG6#F(F 0F0**F'\"\"#F5!\"\"%\"LGF6,&-%$psiG6#F(F0-F26#F(F6F0F0F-F-F-" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "elif D[1](u)(0,t)=phi(t) and u(L,t)=psi(t ) then" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "b:=n->Pi*(2*n-1)/2/L: Xn: =(x,n)->cos(b(n)*x):" }}{PARA 0 "> " 0 "" {XPPEDIT 19 1 "z:=(x,t)->x*p hi(t)+(psi(t)-L*phi(t))" "6#>%\"zGf*6$%\"xG%\"tG7\"6$%)operatorG%&arro wG6\",&*&F'\"\"\"-%$phiG6#F(F0F0,&-%$psiG6#F(F0*&%\"LGF0-F26#F(F0!\"\" F0F-F-F-" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "elif u(0,t)=phi(t) and \+ D[1](u)(L,t)=psi(t) then" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "b:=n->P i*(2*n-1)/2/L: Xn:=(x,n)->sin(b(n)*x):" }}{PARA 0 "> " 0 "" {XPPEDIT 19 1 "z:=(x,t)->phi(t)+x*psi(t)" "6#>%\"zGf*6$%\"xG%\"tG7\"6$%)operato rG%&arrowG6\",&-%$phiG6#F(\"\"\"*&F'F2-%$psiG6#F(F2F2F-F-F-" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "fi:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 53 "\317\360\356\342\345\344\345\354 \342\350\347\363\340\353\350\347 \340\366\350\376 \342\373\341\360\340\355\355\373\365 \361\356\341\361 \362\342\345\355\355\373\365 \347\355\340\367\345\355\350\351 " } {TEXT 289 1 "b" }{TEXT -1 1 "(" }{TEXT 290 1 "n" }{TEXT -1 23 "), \361 \356\341\361\362\342\345\355\355\373\365 \364\363\355\352\366\350\351 \+ " }}{PARA 0 "" 0 "" {TEXT 291 2 "Xn" }{TEXT -1 1 "(" }{TEXT 292 1 "x" }{TEXT -1 1 "," }{TEXT 293 1 "n" }{TEXT -1 12 ") \350 \364\363\355\352 \366\350\350 " }{TEXT 294 1 "z" }{TEXT -1 1 "(" }{TEXT 295 1 "x" } {TEXT -1 1 "," }{TEXT 296 1 "t" }{TEXT -1 2 ")." }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 21 "b(n);Xn(x,n); z(x,t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&%#PiG\"\"\"%\"nGF%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #-%$sinG6#*(%#PiG\"\"\"%\"nGF(%\"xGF(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(\"\"\"F$-%$cosG6#%\"tG!\"\"*&%\"xGF$,&F$F)F%F$F$F$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 81 "\317\360\356\342\345\360\350\354 \355\340 \356\344\355\356\360\356\344\355\356\361\362\374 \357\356\353\363\367 \345\355\355\373\365 \343\360\340\355\350\367\355\373\365 \363\361\353 \356\342\350\351 \344\353\377 \342\342\356\344\350\354\356\351 \342 \+ \357\356\361\353\345\344\363\376\371\345\354 " }}{PARA 0 "" 0 "" {TEXT -1 61 "\364\363\355\352\366\350\350 W(x,t), \342\373\341\360\340 \342 \355\350\346\345 \355\363\346\355\363\376 \361\362\360\356\367 \352\363 \350 \361\355\377\342 \340\357\356\361\362\360\356\364\373. \+ " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "Ww(x,t): Ww(0,t)=u(0,t) -z(0,t); Ww(L,t)=u(L,t)-z(L,t); " }{TEXT -1 2 "1)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%#WwG6$\"\"!%\"tGF'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%#WwG6$\"\"\"%\"tG\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 82 "D[1](Ww)(0,t)=D[1](u)(0,t)-D[1](z)(0,t); D[1](Ww)(L,t)=D[1](u) (L,t)-D[1](z)(L,t); " }{TEXT -1 2 "2)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/--&%\"DG6#\"\"\"6#%#WwG6$\"\"!%\"tG,(--F&6#%\"uGF,F)F)F)-%$cosG6#F .!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/--&%\"DG6#\"\"\"6#%#WwG6$F) %\"tG,(--F&6#%\"uGF,F)F)F)-%$cosG6#F-!\"\"" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 64 "D[1](Ww)(0,t)=D[1](u)(0,t)-D[1](z)(0,t); Ww(L,t)=u( L,t)-z(L,t); " }{TEXT -1 2 "3)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/--& %\"DG6#\"\"\"6#%#WwG6$\"\"!%\"tG,(--F&6#%\"uGF,F)F)F)-%$cosG6#F.!\"\" " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%#WwG6$\"\"\"%\"tG\"\"!" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "Ww(0,t)=u(0,t)-z(0,t); D[1]( Ww)(L,t)=D[1](u)(L,t)-D[1](z)(L,t); " }{TEXT -1 2 "4)" }{MPLTEXT 1 0 3 " " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%#WwG6$\"\"!%\"tGF'" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#/--&%\"DG6#\"\"\"6#%#WwG6$F)%\"tG,(--F &6#%\"uGF,F)F)F)-%$cosG6#F-!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 297 12 "\317\360\350\354\345\367\340\355\350\345. " }{TEXT -1 67 "\307\340 \357\350\370\345\354 \344\353\377 1-\351 \352\360\340\345\342\356\351 \+ \347\340\344\340\367\350 \362\340\352 \355\340\347\373\342\340\345\354 \373\345 \363\361\353\356\342\350\377 \361\356\343\353\340\361\356\342 \340\355\350\377:" }{TEXT 298 1 " " }}{PARA 0 "" 0 "" {TEXT 299 1 "u" }{TEXT -1 6 "(0,0)=" }{TEXT 300 1 "f" }{TEXT -1 4 "(0)=" }{TEXT 301 3 "phi" }{TEXT -1 6 "(0) \350 " }{TEXT 302 1 "u" }{TEXT -1 1 "(" }{TEXT 303 1 "L" }{TEXT -1 4 ",0)=" }{TEXT 304 1 "f" }{TEXT -1 1 "(" }{TEXT 305 1 "L" }{TEXT -1 2 ")=" }{TEXT 306 3 "psi" }{TEXT -1 53 "(0), \342 \373\357\356\353\355\345\355\350\345 \352\356\362\356\360\373\365 \355 \345\353\374\347\377 \361\352\340\347\340\362\374 \356\341\377\347\340 \362\345\353\374\355\356\345, " }}{PARA 0 "" 0 "" {TEXT -1 76 "\355 \356 - \346\345\353\340\362\345\353\374\355\356\345. \310\347\354\345 \355\345\355\350\345 \343\360\340\355\350\367\355\373\365 \363\361\353 \356\342\350\351 \350\347\354\345\355\377\345\362 \363\361\353\356\342 \350\377 \361\356\343\353\340\361\356\342\340\355\350\377." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "if f(0)=phi(0) and f(L)=psi(0) then sogL:=`\363\361\353\356\342\350\377 \361\356\343\353\340\361\356\342 \340\355\350\377 \342\373\357\356\353\355\345\355\373` " }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 51 "else sogL:=`\363\361\353\356\342\350\377 \361 \356\343\353\340\361\356\342\340\355\350\377 \355\345 \342\373\357\356 \353\355\345\355\373` fi: " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 49 " \350 \357\360\350\342\345\344\345\354 \342\350\347\363\340\353\350 \347\340\366\350\376 \350\365 \342\373\357\356\353\355\345\355\350\377 \355\340 \344\350\361\357\353\345\345" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "sogL; " }{TEXT -1 6 "\316\362\342\345\362:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%?|^z|\\z|fy|iy|]y|cy|jz~|\\z|iy|^y|fy|[y|\\ z|iy|]y|[y|hy|cy|jz~|]y|fz|jy|iy|fy|hy|`y|hy|fzG" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 51 "*) \307\340\344\340\344\350\354 \352\356\355\352 \360\345\362\355\363\376 \364\363\355\352\366\350\376 \342\356\347\354 \363\371\345\355\350\377, \355\340\357\360\350\354\345\360:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "g:=(x,t)->sin(x/L); " }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gGf*6$%\"xG%\"tG6\"6$%)operatorG%& arrowGF)-%$sinG6#*&9$\"\"\"%\"LG!\"\"F)F)F)" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 11 "\317\360\350 \375\362\356\354 0<" }{TEXT 307 1 "x" } {TEXT -1 1 "<" }{TEXT 308 1 "L" }{TEXT -1 2 ", " }{TEXT 309 2 " t" } {TEXT -1 66 ">0, \367\362\356 \342\356 \354\355\356\343\356\354 \356 \341\363\361\353\356\342\353\345\355\356 \357\360\345\344\361\362\340 \342\353\345\355\350\345\354 \360\345\370\345\355\350\377 \342 \342 \350\344\345 \360\377\344\340. " }}{PARA 0 "" 0 "" {TEXT -1 80 "\304 \340\353\345\345 \357\356\361\362\360\356\345\355\350\345 \360\345\370 \345\355\350\377 \350\344\345\362 \342 \340\342\362\356\354\340\362 \350\367\345\361\352\356\354 \360\345\346\350\354\345 \342 \361\356 \356\362\342\345\362\361\362\342\350\350 \361 \354\345\362\356\344\350 \352\356\351" }}{PARA 0 "" 0 "" {TEXT -1 82 "\345\343\356 \352\356\354 \357\374\376\362\345\360\355\356\343\356 \350\347\353\356\346\345\355 \350\377 \350 \357\356\347\342\356\353\377\345\362 \342\345\361\362 \350 \344\345\362\340\353\374\355\373\351 \340\355\340\353\350\347, \+ \342 \362\356\354 \367\350\361\353\345 \343\360\340\364\350-" }}{PARA 0 "" 0 "" {TEXT -1 42 "\367\345\361\352\350\351, \352\340\346\344\356 \343\356 \357\360\356\354\345\346\363\362\356\367\355\356\343\356 \360 \345\347\363\353\374\362\340\362\340." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 78 "\320\345\370\345\355\350\345 \350\361\365\356\344\355\356 \343\356 \344\350\364\364\345\360\345\355\366\350\340\353\374\355\356 \343\356 \363\360\340\342\355\345\355\350\377, \363\344\356\342\353 \345\362\342\356\360\377\376\371\345\343\356 \342\373\370\345 \361\364 \356\360\354\363\353\350-" }}{PARA 0 "" 0 "" {TEXT -1 65 "\360\356\342 \340\355\355\373\354 \352\360\340\345\342\373\354 \363\361\353\356\342 \350\377\354, \352\340\352 \341\373\353\356 \361\352\340\347\340\355 \356, \341\363\344\345\354 \350\361\352\340\362\374 \342 \342\350\344 \345 " }}{PARA 0 "" 0 "" {TEXT 311 1 "u" }{TEXT -1 1 "(" }{TEXT 312 1 "x" }{TEXT -1 1 "," }{TEXT 313 1 "t" }{TEXT -1 2 ")=" }{TEXT 314 1 "z " }{TEXT -1 1 "(" }{TEXT 315 1 "x" }{TEXT -1 1 "," }{TEXT 316 1 "t" } {TEXT -1 2 ")+" }{TEXT 317 1 "w" }{TEXT -1 1 "(" }{TEXT 318 1 "x" } {TEXT -1 1 "," }{TEXT 319 1 "t" }{TEXT -1 2 ")+" }{TEXT 320 1 "v" } {TEXT -1 1 "(" }{TEXT 321 1 "x" }{TEXT -1 1 "," }{TEXT 322 1 "t" } {TEXT -1 26 ") \350 \355\340\365\356\344\350\362\374 \350\347 \363\360 \340\342\355\345\355\350\377:" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "de:=a^2*diff(u(x,t),x$2)-diff(u(x,t),t$2)+g(x,t)=0:" "6#>%#deG/, (*&%\"aG\"\"#-%%diffG6$-%\"uG6$%\"xG%\"tG-%\"$G6$F0F)\"\"\"F5-F+6$-F.6 $F0F1-F36$F1F)!\"\"-%\"gG6$F0F1F5\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 30 "\304\353\377 \352\340\346\344\356\351 \352\356\354\357 \356\355\345\355\362\373 \360\345\370\345\355\350\377 " }{TEXT 323 1 " u" }{TEXT -1 1 "(" }{TEXT 324 1 "x" }{TEXT -1 1 "," }{TEXT 325 1 "t" } {TEXT -1 9 "), \352\360\356\354\345 " }{TEXT 326 1 "z" }{TEXT -1 1 "( " }{TEXT 327 1 "x" }{TEXT -1 1 "," }{TEXT 328 1 "t" }{TEXT -1 33 "), \+ \347\340\357\350\370\345\354 \361\342\356\270 \344\350\364\364\345\360 \345\355\366\350\340\353\374\355\356\345 " }}{PARA 0 "" 0 "" {TEXT -1 82 "\363\360\340\342\355\345\355\350\345 \361 \367\340\361\362\355\373 \354\350 \357\360\356\350\347\342\356\344\355\373\354\350, \350\347 \+ \352\356\362\356\360\356\343\356 \356\355\340 \344\356\353\346\355\340 \356\357\360\345\344\345\353\377\362\374\361\377, 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\363\361\353\356\342\350\377 \344\353\377 " }}{PARA 0 "" 0 "" {TEXT -1 8 "\364\363\355\352\366\350 \350 " }{TEXT 377 1 "w" }{TEXT -1 1 "(" }{TEXT 378 1 "x" }{TEXT -1 1 " ," }{TEXT 379 1 "t" }{TEXT -1 2 "):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "f1:=x->f(x)-z(x,0):f1(x); f1(2):" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&%\"xG\"\"\",&F%F%F$!\"\"F%" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 46 "\307\344\345\361\374 F1(x)=F(x)-D[2](z)(x,0). \317\356 \375\362\356\354\363 \350\354\345\345\354:" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 45 "F1:=x->F(x)-D[2](z)(x,0):D[2](z)(x,0); F1(x);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 380 10 "\317\360\350\354\345 \367\340\355\350\345" }{TEXT -1 62 ". \317\360\350 \375\362\356\354 \+ \357\356 \356\357\360\345\344\345\353\345\355\350\376 \350\354\345\345 \354 \355\363\353\345\342\373\345 \343\360\340\355\350\367\355\373\345 \363\361\353\356\342\350\377 \344\353\377 " }{TEXT 381 1 "w" 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-1 50 "\363\357\360\356\371\345\355\350\377 \342 \373\360\340\346\345\355\350\351. \323\352\340\346\345\354 \355\340 \+ \361\342\356\351\361\362\342\356 \357\340\360\340\354\345\362\360\340 \+ " }{TEXT 385 1 "n" }{TEXT -1 22 " \350 \342\342\345\344\345\354 \356 \341\356\347\355\340\367\345\355\350\377:" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 22 "assume(n,integer): " }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 12 "N:=infinity:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 386 26 "2. \307\340\357\350\370\345\354 2-\376 \352\356\354\357\356\355 \345\355\362\363 " }{TEXT 387 1 "w" }{TEXT 388 1 "(" }{TEXT 389 1 "x" }{TEXT 390 1 "," }{TEXT 391 1 "t" }{TEXT 392 10 ") \360\345\370\345 \355\350\377 " }{TEXT 393 1 "u" }{TEXT 394 1 "(" }{TEXT 395 1 "x" } {TEXT 396 1 "," }{TEXT 397 1 "t" }{TEXT 398 1 ")" }{TEXT -1 2 ". " }} {PARA 0 "" 0 "" {TEXT -1 45 "\315\340\367\355\345\354 \361 \342\373 \367\350\361\353\345\355\350\377 \352\356\375\364\364\350\366\350\345 \355\362\356\342 \360\377\344\340 \324\363\360\374\345:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 71 "- \347\340\357\350\370\345\354 \352\356 \375\364\364\350\366\350\345\355\362\373 \360\340\347\353\356\346\345 \355\350\377 \342 \360\377\344 \324\363\360\374\345 \357\356 \361\356 \341\361\362\342\345\355\355\373\354 \347\355\340\367\345\355\350\377 \354 " }{TEXT 399 2 "Xn" }{TEXT -1 1 "(" }{TEXT 400 1 "x" }{TEXT -1 1 "," }{TEXT 401 1 "n" }{TEXT -1 2 ") " }}{PARA 0 "" 0 "" {TEXT -1 9 " \364\363\355\352\366\350\351 " }{TEXT 402 1 "f" }{TEXT -1 2 "1(" } {TEXT 403 1 "x" }{TEXT -1 4 ") \350 " }{TEXT 404 1 "F" }{TEXT -1 2 "1( " }{TEXT 405 1 "x" }{TEXT -1 30 "), \347\340\344\340\376\371\350\365 \+ \355\340\367\340\353\374\355\373\345 \363\361\353\356\342\350\377 " } {TEXT 406 1 "w" }{TEXT -1 1 "(" }{TEXT 407 1 "x" }{TEXT -1 4 ",0):" }} }{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "A:=n->2/L*int(f1(x)*Xn(x,n), \+ x=0..L): A(n);" "6#C$>%\"AGf*6#%\"nG7\"6$%)operatorG%&arrowG6\"*(\"\"# \"\"\"%\"LG!\"\"-%$intG6$*&-%#f1G6#%\"xGF0-%#XnG6$F:F(F0/F:;\"\"!F1F0F -F-F--F%6#F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$**\"\"%\"\"\",&F&!\" \")F(%#n|irGF&F&%#PiG!\"$F*F,F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 82 "*) \305\361\353\350 \345\361\362\374 \342\356\347\354\356\346\355 \356\361\362\374 \363\357\360\356\361\362\350\362\374, \362\356 \361 \353\345\344\363\345\362 \347\340\357\350\361\340\362\374 \357\360\356 \361\362\363\376 \364\356\360\354\363\353\363. \302\356\347\354\356 \346\355\356 " }}{PARA 0 "" 0 "" {TEXT -1 82 "\350\354\345\345\362 \+ \361\354\373\361\353 \357\345\360\345\351\362\350 \352 \342\345\352 \362\356\360\355\356\351 \347\340\357\350\361\350 \352\356\375\364\364 \350\366\350\345\355\362\356\342 \324\363\360\374\345 - \352\340\352 \356\342\373\354\350 \356\355\350 \377\342\353\377\376\362\361\377" }} {PARA 0 "" 0 "" {TEXT -1 66 "\350\347\355\340\367\340\353\374\355\356. \307\344\345\361\374 \344\353\377 \342\361\345\365 \367\345\362\355 \373\365 n \350\354\345\345\354 A(n) = 0, \340 \344\353\377 \355\345 \367\345\362\355\373\365" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "AA[2*n-1]:=A(2*n-1); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%#AAG6#,&* &\"\"#\"\"\"%#n|irGF*F*F*!\"\",$*(\"\")F*%#PiG!\"$,**&F/F*)F+\"\"$F*F* *&\"#7F*)F+F)F*F,*&\"\"'F*F+F*F*F*F,F,F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "A(117); A(118);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$ *(\"\")\"\"\"\"(8;g\"!\"\"%#PiG!\"$F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 576 17 "\315\340 \342\361 \377\352\350\351 \361\353\363\367\340\351:" }}{PARA 0 "" 0 "" {TEXT -1 58 "\317\345\360\345\351\344\270\354 \352 \342\345\352\362\356\360 \355\356\351 \347\340\357\350\361\350 \352\356\375\364\364\350\366\350 \345\355\362\356\342 A(n) \360\377\344\340 \324\363\360\374\345:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "Nv:=5: " }{TEXT -1 26 "- \367 \350\361\353\356 \352\356\354\357\356\355\345\355\362 \342\345\352\362 \356\360\340." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "Av:=vector (Nv,[]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#AvG-%&arrayG6$;\"\"\"\" \"&7\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 46 "\307\340\357\350\370 \345\354 \340\353\343\356\360\350\362\354 \342\373\367\350\361\353\345 \355\350\377 \352\356\354\357\356\355\345\355\362 \342\345\352\362\356 \360\340:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "for m from 1 t o floor(Nv/2) do" }}{PARA 212 "> " 0 "" {MPLTEXT 1 0 38 "Av[2*m-1]:=A( 2*m-1): Av[2*m]:=A(2*m): " }}{PARA 212 "> " 0 "" {MPLTEXT 1 0 38 "if m =floor(Nv/2) and modp(Nv,2)>0 then" }}{PARA 212 "> " 0 "" {MPLTEXT 1 0 17 "Av[Nv]:=A(Nv) fi:" }}{PARA 212 "> " 0 "" {MPLTEXT 1 0 3 "od:" }} }{EXCHG {PARA 0 "" 0 "" {TEXT -1 66 "\317\360\356\342\345\344\270\354 \+ \342\350\347\363\340\353\350\347\340\366\350\376 \350 \357\360\356\342 \345\360\352\363 \342\373\367\350\361\353\345\355\355\373\365 \352\356 \354\357\356\355\345\355\362 \342\345\352\362\356\360\340 Av:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "Av[3]; Av[4]; Av[Nv]; eval( Av);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*(\"\")\"\"\"\"#F!\"\"%#PiG! \"$F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*(\"\")\"\"\"\"$D\"!\"\"%#PiG!\"$F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#K%'vectorG6#7',$*&\"\")\"\"\"%#PiG!\"$F*\"\"!,$*(F)F *\"#F!\"\"F+F,F*F-,$*(F)F*\"$D\"F1F+F,F*Q(pprint06\"" }}}{EXCHG {PARA 256 "" 0 "" {TEXT -1 76 "\307\340\357\350\361\340\355\355\373\351 \340 \353\343\356\360\350\362\354 \357\356\347\342\356\353\377\345\362 \342 \373\367\350\361\353\377\362\374 \352\356\354\357\356\355\345\355\362 \373 \342\345\352\362\356\360\340 Av, \367\350\361\353\356 \352\356 \362\356\360\373\365" }}{PARA 0 "" 0 "" {TEXT 414 28 "\342\361\345\343 \344\340 \360\340\342\355\356 \347\340\344\340\342\340\345\354\356\354 \363 Nv." }{TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT 578 10 "\317\360\350 \354\345\367\340\355\350\345" }{TEXT -1 72 ". \307\344\345\361\374 A(n ) \350\354\345\345\362 \356\341\371\350\351 \342\350\344 n-\343\356 \+ \367\353\345\355\340 \360\377\344\340 \324\363\360\374\345 \350 \355 \350\367\345\354 \355\345 \363\361\362\363\357\340\345\362 \342" }} {PARA 0 "" 0 "" {TEXT -1 57 "\357\360\356\361\362\356\362\345 \347\340 \357\350\361\350 \352\356\354\357\356\355\345\355\362\345 Av[n], \340 \+ \361\352\356\360\345\345 \344\340\346\345 \355\340\356\341\356\360\356 \362." }}{PARA 0 "" 0 "" {TEXT -1 44 "\302\373\367\350\361\353\350\354 \344\360\363\343\356\351 \352\356\375\364\364\350\366\350\345\355\362 B(n) \360\377\344\340 \324\363\360\374\345 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "B:=n->2/(Pi*n*a)*int(F1(x)*Xn(x,n), x=0..L): B(n ); B(2): B(17):" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 85 "\352\356\362\356\360\373\351 \356\352\340 \347\340\353\361\377 \360\340\342\355\373\354 \355\363\353\376 \344 \353\377 \342\361\345\365 n: B(n) = 0. \321\353\345\344\356\342\340 \362\345\353\374\355\356 \352\356\355\342\345\360\362\350\360\356\342 \340\362\374 \375\362\356\362 " }}{PARA 0 "" 0 "" {TEXT -1 81 "\352 \356\375\364\350\366\350\345\355\362 \342 \342\345\352\362\356\360 \+ \355\345 \350\354\345\345\362 \361\354\373\361\353\340. \316\344\355 \340\352\356 \357\360\356\343\360\340\354\354\340 \345\343\356 \352 \356\355\342\345\360\362\350\360\356\342\340\355\350\377 \341\373\353 \340 \341\373" }}{PARA 0 "" 0 "" {TEXT -1 10 "\361\353\345\344\363\376 \371\345\351 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "Bv:=vector (Nv,[]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#BvG-%&arrayG6$;\"\"\"\" \"&7\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "for m from 1 to N v do" }}{PARA 211 "> " 0 "" {MPLTEXT 1 0 13 "Bv[m]:=B(m): " }}{PARA 212 "> " 0 "" {MPLTEXT 1 0 3 "od:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "eval(Bv);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#K%'vector G6#7'\"\"!F'F'F'F'Q(pprint06\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 72 "\302\373\367\350\361\353\350\354 \360\377\344 \357\340\360\340\354 \345\362\360\356\342 \347\340\344\340\367\350 - \361\356\341\361\362 \342\345\355\355\373\345 \367\350\361\353\340 \350 \361\356\341\361 \362\342\345\355\355\373\345 \364\363\355\352\366\350\350" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 " b(n); cos(b(n)*a*t): Xn(x,n); " }} {PARA 11 "" 1 "" {XPPMATH 20 "6#*&%#PiG\"\"\"%#n|irGF%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$sinG6#*(%#PiG\"\"\"%#n|irGF(%\"xGF(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 51 "\322\345\357\345\360\374 \347\340\357\350 \370\345\354 \342\373\360\340\346\345\355\350\345 2-\351 \352\356\354 \357\356\355\345\355\362\373 \357\356\344 \350\354\345\355\345\354 " } {TEXT 408 1 "W" }{TEXT -1 1 "(" }{TEXT 409 1 "x" }{TEXT -1 1 "," } {TEXT 410 1 "t" }{TEXT -1 9 ") \342\354\345\361\362\356 " }{TEXT 411 1 "w" }{TEXT -1 1 "(" }{TEXT 412 1 "x" }{TEXT -1 1 "," }{TEXT 413 1 "t " }{TEXT -1 15 "), \344\353\377 \352\356\362\356\360\356\351 " }} {PARA 0 "" 0 "" {TEXT -1 27 "\350\354\345\345\362\361\377 \361\353\345 \344\363\376\371\340\377 \364\356\360\354\363\353\340: " }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "W:=(x,t)->sum((A(n)*cos(b(n)*a*t)+B(n )*sin(b(n)*a*t))*Xn(x,n), n=1..N):W(x,t);" "6#C$>%\"WGf*6$%\"xG%\"tG7 \"6$%)operatorG%&arrowG6\"-%$sumG6$*&,&*&-%\"AG6#%\"nG\"\"\"-%$cosG6#* (-%\"bG6#F8F9%\"aGF9F)F9F9F9*&-%\"BG6#F8F9-%$sinG6#*(-F?6#F8F9FAF9F)F9 F9F9F9-%#XnG6$F(F8F9/F8;F9%\"NGF.F.F.-F%6$F(F)" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,&*(^#!\"\"\"\"\",*-%(polylogG6$\"\"$-%$expG6#*(%#PiGF' ,&%\"tGF'%\"xGF'F'^#F'F'F'-F*6$F,-F.6#*(F1F',&F3F'F4F&F'F5F'F&-F*6$F,- F.6#*(F%F'F1F'F;F'F'-F*6$F,-F.6#*(F%F'F1F'F2F'F&F'F1!\"$F'*(,*-F*6$F,, $F-F&F'-F*6$F,,$F8F&F&-F*6$F,,$F>F&F'-F*6$F,,$FCF&F&F'F1FFF5F'F'" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 24 "\317\356\361\362\360\356\350\354 \+ \343\360\340\364\350\352 \364\363\355\352\366\350\350 " }{TEXT 418 1 " W" }{TEXT -1 1 "(" }{TEXT 419 1 "x" 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WV(0.5,1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#$!+MO?0D!#5" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 53 "\316\361\356\341\356\343\356 \357\360\345\350\354\363 \371\345\361\362\342\340 \355\350 \356\344\355\340 \350\347 \375\362 \350\365 \364\356\360\354\363\353 \355\345 \350\354\345\345\362." }}} {EXCHG {PARA 0 "" 0 "" {TEXT 460 10 "\317\360\350\354\345\367\340\355 \350\345" }{TEXT -1 71 ". \307\344\345\361\374 \357\356-\357\360\345 \346\355\345\354\363 \367\350\361\353\356 \361\353\340\343\340\345\354 \373\365 \342 \361\363\354\354\345 \360\340\342\355\356 Nv, \355\356 \+ \367\340\361\362\374 \350\347 \355\350\365 -" }}{PARA 0 "" 0 "" {TEXT -1 30 "\355\363\353\345\342\373\345 - \356\362\361\363\362\361\362\342 \363\345\362. \317\356\375\362\356\354\363" }{TEXT 461 1 " " }{TEXT -1 25 "\357\356 \364\340\352\362\363 \354\373 \342\350\344\350\354 \+ \362\356\353\374\352\356 " }{TEXT 577 20 "ceil(Nv/2) \361\353\340\343 \340\345\354\373\365" }{TEXT -1 1 "." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "ceil(Nv/2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"$ " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 44 "*) \307\340\357\350\370\345 \354 \375\362\363 \364\356\360\354\363\353\363 \352\340\352 \364\363 \355\352\366\350\376 \361 \350\354\345\355\345\354 " }{TEXT 527 3 "Wvn " }{TEXT -1 1 "(" }{TEXT 528 1 "x" }{TEXT -1 1 "," }{TEXT 529 1 "t" } {TEXT -1 33 ") \342 \342\350\344\345 \361\363\354\354\373, \361\356 \365\360\340\355\377\377 \357\360\345\346\355\350\354 " }}{PARA 0 "" 0 "" {TEXT -1 28 "\367\350\361\353\356 \345\270 \361\353\340\343\340 \345\354\373\365, \362\356 \345\361\362\374 " }{TEXT 462 10 "ceil(Nv/2 )" }{TEXT -1 2 ": " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 96 "Wvn:= (x,t)->8*sum(cos((2*n-1)*Pi*t)*sin((2*n-1)*Pi*x)/((2*n-1)*Pi)^3, n=1.. ceil(Nv/2));Wvn(x,t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$WvnGf*6$% \"xG%\"tG6\"6$%)operatorG%&arrowGF),$*&\"\")\"\"\"-%$sumG6$**-%$cosG6# *(,&*&\"\"#F0%\"nGF0F0F0!\"\"F0%#PiGF09%F0F0-%$sinG6#*(F9F0F>F09$F0F0F 9!\"$F>FE/F<;F0-%%ceilG6#,$*&F;F=%#NvGF0F0F0F0F)F)F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(**\"\")\"\"\"%#PiG!\"$-%$cosG6#*&F'F&%\"tGF&F&-%$s inG6#*&F'F&%\"xGF&F&F&*&#F%\"#FF&*(F'F(-F*6#,$*(\"\"$F&F'F&F-F&F&F&-F/ 6#,$*(F;F&F'F&F2F&F&F&F&F&*&#F%\"$D\"F&*(F'F(-F*6#,$*(\"\"&F&F'F&F-F&F &F&-F/6#,$*(FHF&F'F&F2F&F&F&F&F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 26 "\310\362\340\352, \342 \357\356\361\353\345\344\355\345\351 \364 \356\360\354\363\353\345 " }{TEXT 585 8 "polylog " }{TEXT -1 52 "\363 \346\345 \355\345\362. \316\367\345\342\350\344\355\356 \350 \344\360 \363\343\356\345, \367\362\356 \375\362\356 \357\360\356\361\362\340 \377 \364\356\360\354\363\353\340," }}{PARA 0 "" 0 "" {TEXT -1 75 " \350\354\345\376\371\340\377 \361\353\345\344\363\376\371\363\376 \347 \340\357\350\361\374, \355\345 \347\340\342\350\361\377\371\363\376 \+ \356\362 \350\354\270\355 A(n), B(n) \350 \342\345\352\362\356\360\340 Av. \304\340 " }}{PARA 0 "" 0 "" {TEXT -1 67 "\350 \342\345\360\365 \355\350\351 \357\360\345\344\345\353 Nv \363 \361\363\354\354\373 \+ \354\356\346\345\362 \341\373\362\374 \353\376\341\373\354 \350 \344 \356\361\362\340\362\356\367\355\356 \341\356\353\374\370\350\354. " } }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 25 "\317\356\361\362\360\356\350\354 \343\360\340\364\350\352 \364\363\355\352\366\350\350 " }{TEXT 586 3 "Wvn" }{TEXT -1 1 "(" }{TEXT 587 1 "x" }{TEXT -1 1 "," }{TEXT 588 1 "t" }{TEXT -1 1 ")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "plot3 d(Wvn(x,t), x=0..L+2, t=0..6,axes=boxed,orientation=[-43,36]);" }} {PARA 13 "" 1 "" {GLPLOT3D 496 212 212 {PLOTDATA 3 "6&-%%GRIDG6%;$\"\" !F($\"\"$F(;F'$\"\"'F(X4%)anythingG6\"6\"[gl'!%\"!!#\\bm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-1 1 "(" }{TEXT 464 1 "x" }{TEXT -1 1 "," }{TEXT 465 1 "t" }{TEXT -1 1 ")" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 82 "\312\340 \352 \350 \356\346\350\344\340\353\356\361\374, \"\344\373\360\356\352 \" \363\346\345 \355\345\362. \317\360\350 \375\362\356\354 \343\360 \340\364\350\352 \355\345 \347\340\342\350\361\350\362, \367\362\356 \+ \356\367\345\355\374 \342\340\346\355\356, \356\362 " }}{PARA 0 "" 0 " " {TEXT -1 75 "\367\350\361\353\340 Nv. \317\356\361\353\345\344\355 \345\345 \354\356\346\355\356 \353\345\343\352\356 \357\360\356\342 \345\360\350\362\374 \342 \350\355\362\345\360\340\352\362\350\342\355 \356\354 \360\345\346\350\354\345. \300 \364\363\355\352\366\350\377" }}{PARA 0 "" 0 "" {TEXT 530 3 "Wvn" }{TEXT -1 1 "(" }{TEXT 531 1 "x" } {TEXT -1 1 "," }{TEXT 532 1 "t" }{TEXT -1 71 "), \352\340\352 \341\373 \353\356 \357\356\352\340\347\340\355\356 \342\373\370\345, \354\356 \346\345\362 \341\373\362\374 \347\340\357\350\361\340\355\340 \352 \356\354\357\340\352\362\355\356 \342 \342\350\344\345 \361\363\354 \354\373. " }}}{EXCHG {PARA 0 "" 0 "" {TEXT 606 31 "\302\333\302\316 \304: \344\353\377 \340\353\343\360\350\362\354\350\347\340\366\350 \350 \353\363\367\370\345 " }{TEXT -1 1 "(" }{TEXT 607 8 "\355\345 \+ \344\363\354\340\377" }{TEXT -1 1 ")" }{TEXT 608 26 " \341\360\340\362 \374 Wv(x,t) \350\353\350 WV(x,t)" }{TEXT -1 1 "." }}}{EXCHG {PARA 0 " " 0 "" {TEXT 430 26 "3. \307\340\357\350\370\345\354 3-\376 \352\356 \354\357\356\355\345\355\362\363 " }{TEXT 432 1 "v" }{TEXT 433 1 "(" } {TEXT 434 1 "x" }{TEXT 435 1 "," }{TEXT 436 1 "t" }{TEXT 437 10 ") \+ \360\345\370\345\355\350\377 " }{TEXT 438 1 "u" }{TEXT 439 1 "(" } {TEXT 440 1 "x" }{TEXT 441 1 "," }{TEXT 442 1 "t" }{TEXT 443 1 ")" } {TEXT -1 1 "." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 11 "\312\356\354\357 \356\355\345\355\362\363 " }{TEXT 444 1 "v" }{TEXT -1 1 "(" }{TEXT 445 1 "x" }{TEXT -1 1 "," }{TEXT 446 1 "t" }{TEXT -1 34 ") \361\353 \345\344\363\345\362 \356\357\360\345\344\345\353\377\362\374 \350\347 \363\360\340\342\355\345\355\350\377:" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "dev := a^2*diff(v(x,t),`$`(x,2))-diff(v(x,t),`$`(t,2))+ g1(x,t) = 0:" "6#>%$devG/,(*&%\"aG\"\"#-%%diffG6$-%\"vG6$%\"xG%\"tG-% \"$G6$F0F)\"\"\"F5-F+6$-F.6$F0F1-F36$F1F)!\"\"-%#g1G6$F0F1F5\"\"!" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 81 "\301\363\344\345\354 \342\373\367 \350\361\353\377\362\374 \375\362\363 \352\356\354\357\356\355\345\355 \362\363, \352\340\352 \341\373\353\356 \361\352\340\347\340\355\356 \+ \342\373\370\345, \357\356\353\340\343\340\377 \355\363\353\345\342 \373\354\350 \352\360\340\345\342\373\345 " }}{PARA 0 "" 0 "" {TEXT -1 13 "\363\361\353\356\342\350\377 \344\353\377 " }{TEXT 447 1 "v" } {TEXT -1 1 "(" }{TEXT 448 1 "x" }{TEXT -1 1 "," }{TEXT 449 1 "t" } {TEXT -1 66 "), \367\362\356 \362\340\352\346\345 \357\360\345\344\356 \357\360\345\344\345\353\345\355\356 \342\373\341\356\360\356\354 \361 \356\341\361\362\342\345\355\355\373\365 \364\363\355\352\366\350\351. \310\361\365\356\344\377 \350\347" }}{PARA 0 "" 0 "" {TEXT -1 16 " \342\373\341\356\360\340 \364\363\355\352\366\350\350 " }{TEXT 450 1 "z" }{TEXT -1 1 "(" }{TEXT 451 1 "x" }{TEXT -1 1 "," }{TEXT 452 1 "t" }{TEXT -1 26 "), \343\360\340\355\350\367\355\373\345 \363\361\353\356 \342\350\377 \344\353\377 " }{TEXT 453 1 "v" }{TEXT -1 1 "(" }{TEXT 454 1 "x" }{TEXT -1 1 "," }{TEXT 455 1 "t" }{TEXT -1 26 ") \341\363 \344\363\362 \362\340\352\346\345 \356\344\355\356\360\356\344\355\373 \354\350." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 55 "3.1. \302\373\367 \350\361\353\350\354 \352\356\375\364\364\350\366\350\345\355\362\373 \+ \360\377\344\340 \324\363\360\374\345 \344\353\377 \375\362\356\351 \+ \364\363\355\352\366\350\350:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 80 " - \352\356\375\364\364\350\366\350\345\355\362 \360\377\344\340 \324 \363\360\374\345 \364\363\355\352\366\350\350, \347\340\344\340\376 \371\345\351 \342\356\347\354\363\371\345\355\350\345, \354\356\346 \345\362 \341\373\362\374 \357\360\345\344\361\362\340\342\353\345\355 \342 " }}{PARA 0 "" 0 "" {TEXT -1 5 "\342\350\344\345:" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "q:=(n,t)->2/L*int(g1(x,t)*Xn(x,n), x= 0..L): q(n,t);" "6#C$>%\"qGf*6$%\"nG%\"tG7\"6$%)operatorG%&arrowG6\"*( \"\"#\"\"\"%\"LG!\"\"-%$intG6$*&-%#g1G6$%\"xGF)F1-%#XnG6$F;F(F1/F;;\" \"!F2F1F.F.F.-F%6$F(F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*,\"\"#\" \"\",(*(-%$cosG6#%\"tGF&)%#PiGF%F&)%#n|irGF%F&F&F)!\"\"**F-F&F/F&)F1F0 F&-%$sinG6#F&F&F&F&F.F1F0F1,&*&F-F&F/F&F&F&F1F1F1" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 14 "\302\342\345\344\270\354 \342\345\352\362\356\360 \+ " }{TEXT 466 2 "qv" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "qv:=v ector(Nv,[]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#qvG-%&arrayG6$;\" \"\"\"\"&7\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 49 "\350 \342\373\367 \350\361\353\350\354 \345\343\356 \352\356\354\357\356\355\345\355\362 \373 \357\356 \361\353\345\344\363\376\371\345\354\363 \340\353\343 \356\360\350\362\354\363" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "for n1 from 1 to Nv do" }}{PARA 212 "> " 0 "" {MPLTEXT 1 0 15 "qv[n1] :=q(n1,t)" }}{PARA 212 "> " 0 "" {MPLTEXT 1 0 3 "od:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 51 "\317\360\356\342\345\344\270\354 \342\350\347 \363\340\353\350\347\342\366\350\376 \350 \357\360\356\342\345\360\352 \363 \352\356\354\357\356\355\345\355\362 \342\345\352\362\356\360\340 " }{TEXT 467 2 "qv" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "qv[N v]; eval(qv):" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&#\"\"#\"\"&\"\"\" *(,(*(\"#DF(-%$cosG6#%\"tGF()%#PiGF&F(!\"\"F-F(*(F,F(-%$sinG6#F(F(F1F( F(F(F2F3,&*&F,F(F1F(F(F(F3F3F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 45 "3.2. \310, \355\340\352\356\355\345\366, \347\340\357\350\370\345 \354 \361\340\354\363 3-\376 \352\356\354\357\356\355\345\355\362\363 \+ " }{TEXT 456 1 "v" }{TEXT -1 1 "(" }{TEXT 457 1 "x" }{TEXT -1 1 "," } {TEXT 458 1 "t" }{TEXT -1 29 "), \350\361\357\356\353\374\347\363\377 \+ \364\356\360\354\363\353\363 \360\345\370\345\355\350\377 " }}{PARA 0 "" 0 "" {TEXT -1 10 "\363\360\340\342\355\345\355\350\377 " }{TEXT 459 3 "dev" }{TEXT -1 1 ":" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "v:=(x,t)->sum((int(q(n2,tau)*sin(b(n2)*a*(t-tau)), tau=0..t)*Xn(x,n2) /(b(n2)*a)), n2=1..N): simplify(v(x,t));" "6#C$>%\"vGf*6$%\"xG%\"tG7\" 6$%)operatorG%&arrowG6\"-%$sumG6$*(-%$intG6$*&-%\"qG6$%#n2G%$tauG\"\" \"-%$sinG6#*(-%\"bG6#F:F<%\"aGF<,&F)F " 0 "" {MPLTEXT 1 0 93 "vN:=(x,t)->sum((int(q(n2,ta u)*sin(b(n2)*a*(t-tau)), tau=0..t)*Xn(x,n2)/(b(n2)*a)), n2=1..Nv);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#vNGf*6$%\"xG%\"tG6\"6$%)operatorG%& arrowGF)-%$sumG6$,$-%$intG6$*&-%\"qG6$%#n2G%$tauG\"\"\"-%$sinG6#*(-%\" bG6#F8F:%\"aGF:,&9%F:F9!\"\"F:F:/F9;\"\"!FD*(-%#XnG6$9$F8F:F?FEFBFE/F8 ;F:%#NvGF)F)F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 68 "\307\344\345 \361\374 \357\356\344 \347\355\340\352\356\354 \350\355\362\345\343 \360\340\353\340 \361\362\356\350\362 q(n2,tau) = qv[nn] (\361\354. \+ \342\373\370\345), \343\344\345:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 86 "qv[nn]=-2*(-cos(tau)+cos(tau)*Pi^2*nn^2+Pi^2*nn^2*(-1 )^nn*sin(1))/Pi/nn/(Pi^2*nn^2-1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/ &%#qvG6#%#nnG,$*,\"\"#\"\"\",(-%$cosG6#%$tauG!\"\"*(F-F+)%#PiGF*F+)F'F *F+F+**F3F+F5F+)F1F'F+-%$sinG6#F+F+F+F+F4F1F'F1,&*&F3F+F5F+F+F+F1F1F1 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "InT:=Int(qv[n2]*sin(b(n 2)*a*(t-tau)),tau=0..t); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$InTG-% $IntG6$*&&%#qvG6#%#n2G\"\"\"-%$sinG6#*(%#PiGF-F,F-,&%\"tGF-%$tauG!\"\" F-F-/F5;\"\"!F4" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 82 "\302\373\367 \350\361\353\350\354 \356\362\344\345\353\374\355\356 \350\355\362\345 \343\360\340\353 InT, \361 \357\356\344\361\362\340\355\356\342\352 \356\351 \357\356\344 \347\355\340\352 \350\355\362\345\343\360\340 \353\340 \342\373\360\340\346\345\355\350\377 qv[nn]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "assume(nn,integer): about(nn);" }}{PARA 6 "" 1 "" {TEXT -1 27 "Originally nn, renamed nn~:" }}{PARA 6 "" 1 "" {TEXT -1 27 " is assumed to be: integer" }}{PARA 6 "" 1 "" {TEXT -1 0 "" }}{PARA 6 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "InT:=(nn,t)->int(-2*(-cos(tau)+cos(tau)*Pi^2*nn^2+Pi^2* nn^2*(-1)^nn*sin(1))/Pi/nn/(Pi^2*nn^2-1)*sin(b(nn)*a*(t-tau)),tau=0..t ):" "6#>%$InTGf*6$%#nnG%\"tG7\"6$%)operatorG%&arrowG6\"-%$intG6$,$*.\" \"#\"\"\",(-%$cosG6#%$tauG!\"\"*(-F76#F9F4*$%#PiGF3F4*$F'F3F4F4**F?F3* $F'F3F4),$F4F:F'F4-%$sinG6#F4F4F4F4F?F:F'F:,&*&F?F3*$F'F3F4F4F4F:F:-FF 6#*(-%\"bG6#F'F4%\"aGF4,&F(F4F9F:F4F4F:/F9;\"\"!F(F-F-F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "simplify(InT(n,t));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*(\"\"#\"\"\",&*&)%#PiGF%F&)%#n|irGF%F&F&F&!\"\" F-,*-%$cosG6#*(F,F&F*F&%\"tGF&F&*(F/F&)F-F,F&-%$sinG6#F&F&F&-F06#F3F-* &)F-,&F,F&F&F&F&F6F&F&F&F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 25 " \302\342\345\344\270\354 \355\356\342\356\270 \350\354\377 \364\363 \355\352\366\350\350 " }{TEXT 533 3 "vNN" }{TEXT -1 1 "(" }{TEXT 534 1 "x" }{TEXT -1 1 "," }{TEXT 535 1 "t" }{TEXT -1 40 ") \342 \356\362 \353\350\367\350\345 \356\362 \360\340\355\345\345 \356\357\350\361 \340\355\355\356\351 vN(x,t)." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 42 "\302\342\345\344\270\354 \342\345\352\362\356\360 \352\356\354\357 \356\355\345\355\362 \361\363\354\354\373 \344\353\377 \364\363\355 \352\366\350\350 " }{TEXT 536 3 "vNN" }{TEXT -1 1 "(" }{TEXT 537 1 "x " }{TEXT -1 1 "," }{TEXT 538 1 "t" }{TEXT -1 1 ")" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 18 "Sv:=vector(Nv,[]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#SvG-%&arrayG6$;\"\"\"\"\"&7\"" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 21 "for j from 1 to Nv do" }}{PARA 211 "> " 0 "" {MPLTEXT 1 0 42 "Sv[j]:=subs(n=j,InT(n,t)*Xn(x,n)/b(n)/a): " }}{PARA 212 "> " 0 "" {MPLTEXT 1 0 3 "od:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 19 "\316\344\355\340\352\356 \356\357\360\345\344\345\353\345\355\350 \345 " }{TEXT 539 3 "vNN" }{TEXT -1 1 "(" }{TEXT 540 1 "x" }{TEXT -1 1 "," }{TEXT 541 1 "t" }{TEXT -1 36 ") = sum(Sv[j], j = 1..Nv) \355 \345 \342\342\356\344\350\362 " }{TEXT 542 3 "vNN" }{TEXT -1 1 "(" } {TEXT 543 1 "x" }{TEXT -1 1 "," }{TEXT 544 1 "t" }{TEXT -1 18 ") \352 \340\352 \364\363\355\352\366\350\376, \344\353\377" }}{PARA 0 "" 0 " " {TEXT -1 83 "\367\345\343\356 \361\356\341\361\362\342\345\355\355 \356 \375\362\356 \350 \344\345\353\340\353\356\361\374, \367\362\356 \+ \342 \344\340\353\374\355\345\351\370\345\354 \356\352\340\347\373\342 \340\345\362\361\377 \355\345\363\344\356\341\355\373\354. \317\356 \375\362\356\354\363 \356\362 " }}{PARA 0 "" 0 "" {TEXT -1 80 "\375 \362\356\343\356 \361\353\345\344\363\345\362 \356\362\352\340\347\340 \362\374\361\377, \345\361\353\350 \355\345 \356\357\360\345\344\345 \353\350\362\374 \352\356\354\357\356\355\345\355\362\363 \342\345\352 \362\356\360\340 Sv \352\340\352 \364\363\355\352\366\350\376. " }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "Sv[1]; Sv[2]: eval(Sv):" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#,$*,\"\"#\"\"\",*-%$cosG6#*&%#PiGF&%\" tGF&F&*&F(F&-%$sinG6#F&F&!\"\"-F)6#F-F2F/F&F&,&*$)F,F%F&F&F&F2F2-F06#* &F,F&%\"xGF&F&F,F2F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 601 12 "\316\357 \360\345\344\345\353\345\355\350\345 " }{TEXT 589 3 "vNN" }{TEXT 602 1 "(" }{TEXT 590 1 "x" }{TEXT 603 1 "," }{TEXT 591 1 "t" }{TEXT 604 13 ") \352\340\352 \364\363\355\352\366\350\350" }{TEXT -1 1 "." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 43 "\316\357\360\345\344\345\353\350\354 \352 \356\354\357\356\355\345\355\362\363 \342\345\352\362\356\360\340 sv \+ \352\340\352 \364\363\355\352\366\350\376" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 61 "sv:=(x,t)->vector(Nv,[seq(InT(n,t)*Xn(x,n)/b(n)/a,n =1..Nv)]):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 36 "\350 \357\360\356 \342\345\344\270\354 \342\373\367\350\361\353\345\355\350\345 \345\343 \356 \352\356\354\357\356\355\345\355\362:" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 53 "eval(sv(x,t)): sv(x,t)[1];sv(x,t)[2]; sv(0.25,1)[2 ];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*,\"\"#\"\"\",*-%$cosG6#*&%#Pi GF&%\"tGF&!\"\"*&F(F&-%$sinG6#F&F&F&-F)6#F-F&F0F.F&,&*$)F,F%F&F&F&F.F. -F16#*&F,F&%\"xGF&F&F,F.F." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#**,,*(\" \"#\"\"\"-%$sinG6#F'F')-%$cosG6#*&%#PiGF'%\"tGF'F&F'F'*&F&F'F(F'!\"\"* &F&F'F+F'F'F'F3-F-6#F1F3F',&*&\"\"%F')F0F&F'F'F'F3F3-F)6#,$*(F&F'F0F'% \"xGF'F'F'F0F3" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*(,&\"\"\"!\"\"-%$ cosG6#F&F&F&,&*&\"\"%F&)%#PiG\"\"#F&F&F&F'F'F/F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "simplify(sv(x,t)[3]-Sv[3]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 39 "\322 \345\357\345\360\374 \354\356\346\355\356 \356\357\360\345\344\345\353 \350\362\374 \350 \361\340\354\363 \364\363\355\352\366\350\376 " } {TEXT 592 3 "vNN" }{TEXT -1 1 "(" }{TEXT 593 1 "x" }{TEXT -1 1 "," } {TEXT 594 1 "t" }{TEXT -1 27 "), \355\356 \363\346\345 \357\356\344 \+ \355\356\342\373\354 \350\354\345\355\345\354 " }{TEXT 595 3 "vnn" } {TEXT -1 1 "(" }{TEXT 596 1 "x" }{TEXT -1 1 "," }{TEXT 597 1 "t" } {TEXT -1 1 ")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "vnn:=(x,t) ->sum(sv(x,t)[jj], jj=1..Nv); vnn(x,t):" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$vnnGf*6$%\"xG%\"tG6\"6$%)operatorG%&arrowGF)-%$sumG6$&-%#svG6 $9$9%6#%#jjG/F7;\"\"\"%#NvGF)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "vnn(0,0); evalf(vnn(0.5,1)); " }{TEXT -1 21 "- \" \342\350\344\350\362\" \357\345\360\345\354\345\355\355\373\345." }} {PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+XMGn**!#7" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 8 "\324\363\355 \352\366\350\377 " }{TEXT 598 3 "vnn" }{TEXT -1 1 "(" }{TEXT 599 1 "x " }{TEXT -1 1 "," }{TEXT 600 1 "t" }{TEXT -1 64 ") \360\345\340\343 \350\360\363\345\362 \355\340 \350\347\354\345\355\345\355\350\377 \+ \357\345\360\345\354\345\355\355\373\365, \367\362\356 \350 \362\360 \345\341\356\342\340\353\356\361\374 \357\356\352\340\347\340\362\374. " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 31 "\307\340\357\350\370\345\354 \+ \361\340\354\363 3-\376 \352\356\354\357\356\355\345\355\362\363 - " }{TEXT 490 1 "v" }{TEXT -1 1 "(" }{TEXT 491 1 "x" }{TEXT -1 1 "," } {TEXT 492 1 "t" }{TEXT -1 13 "), \355\356 \357\360\345\346\344\345:" } }{PARA 0 "" 0 "" {TEXT -1 24 "\317\356\361\362\360\356\350\354 \343 \360\340\364\350\352 \364\363\355\352\366\350\350 " }{TEXT 484 3 "vnn " }{TEXT -1 1 "(" }{TEXT 485 1 "x" }{TEXT -1 1 "," }{TEXT 486 1 "t" } {TEXT -1 33 "), \357\360\345\344\361\362\340\342\353\377\376\371\345 \351 3-\376 \352\356\354\357\356\355\345\355\362\363 " }{TEXT 493 1 "v " }{TEXT -1 1 "(" }{TEXT 494 1 "x" }{TEXT -1 1 "," }{TEXT 495 1 "t" } {TEXT -1 8 "), \355\356 \361 " }}{PARA 0 "" 0 "" {TEXT -1 80 "\356\343 \360\340\355\350\367\345\355\355\373\354 \367\350\361\353\356\354 \361 \353\340\343\340\345\354\373\365. \322\340\352\340\377 \340\357\357 \360\356\352\361\350\354\340\366\350\377 \361\377\347\340\355\340 \361 \354\350\355\350\354\350\347\340\366\350\345\351 \342\360\345\354\345 \355\350" }}{PARA 0 "" 0 "" {TEXT -1 6 "\361\367\345\362\340." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "plot3d(vnn(x,t), x=0..L, t=0 ..4,axes=boxed,orientation=[-43,36]);" }}{PARA 13 "" 1 "" {GLPLOT3D 550 290 290 {PLOTDATA 3 "6&-%%GRIDG6%;$\"\"!F($\"\"\"F(;F'$\"\"%F(X4%) anythingG6\"6\"[gl'!%\"!!#\\bm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DF3F8F75C7E712223D3F942FB7CFCFFD393F9508D4E2B224B93F94887EFA3E50933F90 60802A352C8E3F898DE056F05F6D3F90C23578C46D533F95493462519B283F96233330 45C6F23F959BEBB3C12C713F916ED58864C40C3F8AF5933279AF0A393559FE5D5E55B6 3C840C86699159003C95E9CE3B3CD03A3C9743D141273DD03C95DB1F7E915C553C840D E79B7AB6C33C4C0494226D17E23C911A0F4CE619873CA1E792A4B2613B3CA5DAE184B8 D2163CA8244F75A1627D3CA4CB6E030BACA73CA1F137E86A96323CA89DF9A98AB9433C AFAE484EA748F53CB07365875B68743CB01386E4218A4C3CA99AFEBB463C2E3CA3D386 46B6CA803CAA32DCB498A87F3CB0A94A245812B33CB14ED686F6D9313CB0F22E09518D 5E3CAB438F116BD6A93CA4F387B98CF933-%+AXESLABELSG6%%\"xG%\"tGQ!F1-%*AXE SSTYLEG6#%$BOXG-%+PROJECTIONG6%$!#VF($\"#OF(F*" 1 2 0 1 10 0 2 1 1 2 2 1.000000 36.000000 -43.000000 1 0 "Curve 1" }}}}{EXCHG {PARA 257 "" 0 "" {TEXT -1 46 " \320\350\361. . \303\360\340 \364\350\352 \364\363\355\352\366\350\350 " }{TEXT 487 3 "vNN" }{TEXT -1 1 "(" }{TEXT 488 1 "x" }{TEXT -1 1 "," }{TEXT 489 1 "t" }{TEXT -1 2 ") " }}}{EXCHG {PARA 0 "" 0 "" {TEXT 496 51 "4. \310\362\340\352, \+ \350\354\345\345\354 \360\345\370\345\355\350\345 \344\350\364\364\345 \360\345\355\366\350\340\353\374\355\356\343\356 \363\360\340\342\355 \345\355\350\377 " }{TEXT 497 2 "de" }{TEXT 498 21 " \342 \356\352\356 \355\367\340\362\345\353\374\355\356\354 \342\350\344\345" }}{PARA 0 " " 0 "" {TEXT 519 37 "\344\353\377 \356\343\360\340\355\350\367\345\355 \355\356\343\356 \367\350\361\353\340 Nv \361\353\340\343\340\345\354 \373\365:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "`U:=(x,t)->z(x ,t)+W(x,t)+v(x,t); U(x,t):=simplify(U(x,t))`:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 82 "\310\361\365\356\344\377 \350\347 \375\362\356\351 \+ \347\340\357\350\361\350 \350 \357\360\345\344\361\362\340\342\353\345 \355\350\377 \360\345\370\345\355\350\377 \355\345\356\344\355\356\360 \356\344\355\356\343\356 \342\356\353\355\356\342\356\343\356 \363\360 \340\342\355\345\355\350\377 \361 " }}{PARA 0 "" 0 "" {TEXT -1 78 " \356\341\371\350\354\350 \352\360\340\345\342\373\354\350 \363\361\353 \356\342\350\377\354\350, \355\345\353\374\347\377 \357\356\353\363 \367\350\362\374 \347\340 \356\341\356\347\360\350\354\356\345 \342 \360\345\354\377 \345\343\356 \343\360\340\364\350\367\345\361\352\363 \376 " }}{PARA 0 "" 0 "" {TEXT -1 64 "\350\353\353\376\361\362\360\340 \366\350\376. \317\356\375\362\356\354\363 \357\356\361\362\363\357 \350\354 \361\353\345\344\363\376\371\350\354 \356\341\360\340\347\356 \354: \357\345\360\345\367\350\361\353\350\354 \342\361\345 " }}{PARA 0 "" 0 "" {TEXT -1 77 "\340\357\357\360\356\352\361\350\354\350\360 \363\376\371\350\345 \361\356\361\362\340\342\353\377\376\371\350\345 \+ \360\345\370\345\355\350\377 z(x,t), Wv(x,t) (\350\353\350 WV(x,t)), v nn(x,t)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "z(x,t); Wv(x,t); vnn(x,t):" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(\"\"\"F$-%$cosG6#%\"tG! \"\"*&%\"xGF$,&F$F)F%F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(**\" \")\"\"\"%#PiG!\"$-%$cosG6#*&F'F&%\"tGF&F&-%$sinG6#*&F'F&%\"xGF&F&F&*& #F%\"#FF&*(F'F(-F*6#,$*(\"\"$F&F'F&F-F&F&F&-F/6#,$*(F;F&F'F&F2F&F&F&F& F&*&#F%\"$D\"F&*(F'F(-F*6#,$*(\"\"&F&F'F&F-F&F&F&-F/6#,$*(FHF&F'F&F2F& F&F&F&F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 11 "*) \307\340\357\350 \370\345\354 " }{TEXT 499 1 "N" }{TEXT -1 70 "v \367\340\361\362\350 \367\355\363\376 \361\363\354\354\363 \360\345\370\345\355\350\377, \+ \350\361\357\356\353\374\347\363\377 \360\340\355\345\345 \355\340\351 \344\345\355\355\373\345 \344\353\377 \355\345\270 \364\363\355\352 \366\350\350:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "Un:=(x,t)- >z(x,t)+Wv(x,t)+vnn(x,t); Un(x,t); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #>%#UnGf*6$%\"xG%\"tG6\"6$%)operatorG%&arrowGF),(-%\"zG6$9$9%\"\"\"-%# WvGF0F3-%$vnnGF0F3F)F)F)" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,8\"\"\"F$ -%$cosG6#%\"tG!\"\"*&%\"xGF$,&F$F)F%F$F$F$**\"\")F$%#PiG!\"$-F&6#*&F/F $F(F$F$-%$sinG6#*&F/F$F+F$F$F$*&#F.\"#FF$*(F/F0-F&6#,$*(\"\"$F$F/F$F(F 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}}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "UN:=(x,t)->1-cos(t) -x+x*cos(t)+8*sum(cos((2*n-1)*Pi*t)*sin((2*n-1)*Pi*x)/((2*n-1)*Pi)^3, \+ n=1..ceil(Nv/2))+sum(-2*(-cos(Pi*n*t)-cos(Pi*n*t)*(-1)^n*sin(1)+cos(t) +(-1)^n*sin(1))*sin(Pi*n*x)/(Pi^2*n^2-1)/Pi/n,n=1..Nv):" "6#>%#UNGf*6$ %\"xG%\"tG7\"6$%)operatorG%&arrowG6\",.\"\"\"F/-%$cosG6#F(!\"\"F'F3*&F 'F/-F16#F(F/F/*&\"\")F/-%$sumG6$*(-F16#*(,&*&\"\"#F/%\"nGF/F/F/F3F/%#P iGF/F(F/F/-%$sinG6#*(,&*&FBF/FCF/F/F/F3F/FDF/F'F/F/*$*&,&*&FBF/FCF/F/F /F3F/FDF/\"\"$F3/FC;F/-%%ceilG6#*&%#NvGF/FBF3F/F/-F:6$,$*.FBF/,*-F16#* (FDF/FCF/F(F/F3*(-F16#*(FDF/FCF/F(F/F/),$F/F3FCF/-FF6#F/F/F3-F16#F(F/* &),$F/F3FCF/-FF6#F/F/F/F/-FF6#*(FDF/FCF/F'F/F/,&*&FDFB*$FCFBF/F/F/F3F3 FDF3FCF3F3/FC;F/FVF/F-F-F-" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 81 " \335\362\356 \344\342\345 \361\356\342\345\360\370\345\355\355\356 \+ \360\340\342\355\356\347\355\340\367\355\373\345 \364\356\360\354\363 \353\373 Un(x,t) = UN(x,t), \342 \367\270\354 \354\356\346\355\356 \+ 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