{VERSION 6 0 "IBM INTEL NT" "6.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 236 0 76 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 48 37 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 256 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 257 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 258 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 259 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 260 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 261 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 262 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 263 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 264 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 265 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 266 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 267 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 268 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 269 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 270 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 271 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 272 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 273 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 274 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 275 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 276 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 277 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 278 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 279 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 280 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 281 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 282 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 283 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 284 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 285 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 286 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 287 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 288 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 289 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Headi ng 2" -1 4 1 {CSTYLE "" -1 -1 "Times" 1 14 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 4 4 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 12 1 {CSTYLE "" -1 -1 "Ti mes" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 3 0 0 0 0 1 0 1 0 2 2 0 1 } {PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Normal" -1 256 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 4 "" 0 "" {TEXT 256 14 "Cap11_Ejemplo1" }{TEXT -1 46 "\n\nVamos integrar a modo de ejemplo el problema" }}{PARA 4 "" 0 "" {TEXT -1 4 " " }{XPPEDIT 18 0 "delta^2 u/(delta x^2" "6#*(%& deltaG\"\"#%\"uG\"\"\"*&F$F'*$%\"xGF%F'!\"\"" }{TEXT -1 4 " + " } {XPPEDIT 18 0 "delta^2 u/(delta y^2)" "6#*(%&deltaG\"\"#%\"uG\"\"\"* &F$F'*$%\"yGF%F'!\"\"" }{TEXT -1 5 " = 0" }}{PARA 4 "" 0 "" {TEXT -1 61 "en el rect\341ngulo [0,1]x[0,1] , con la condici\363n de contorno " }}{PARA 4 "" 0 "" {TEXT -1 25 " u(0,y)=0 , u(1,y)=y ," }}{PARA 4 "" 0 "" {TEXT -1 30 " u(x,0)=0 , u(x,1)=x . " }}{PARA 4 "" 0 "" {TEXT -1 63 "Como es f\341cil comprobar, este problema tiene la sol uci\363n exacta" }}{PARA 4 "" 0 "" {TEXT -1 14 " u(x,y)=x y" }} {PARA 4 "" 0 "" {TEXT -1 71 "Para nuestros c\341lculos, dividimos [0, 1] para x en N subintervalos" }}{PARA 4 "" 0 "" {TEXT -1 7 "toman do" }}{PARA 4 "" 0 "" {TEXT -1 10 " h = " }{XPPEDIT 18 0 "(b-a)/N " "6#*&,&%\"bG\"\"\"%\"aG!\"\"F&%\"NGF(" }{TEXT -1 3 " = " }{XPPEDIT 18 0 "1/N" "6#*&\"\"\"F$%\"NG!\"\"" }{TEXT -1 33 " \+ " }}{PARA 4 "" 0 "" {TEXT -1 7 "y luego" }}{PARA 4 "" 0 " " {TEXT -1 4 " " }{XPPEDIT 18 0 "x[n]" "6#&%\"xG6#%\"nG" }{TEXT -1 12 " = 0. + n h" }}{PARA 4 "" 0 "" {TEXT -1 5 "o sea" }}{PARA 4 "" 0 "" {TEXT -1 4 " " }{XPPEDIT 18 0 "x[0]" "6#&%\"xG6#\"\"!" }{TEXT -1 9 " = 0. , " }{XPPEDIT 18 0 "x[1]" "6#&%\"xG6#\"\"\"" }{TEXT -1 10 " = 0.2 , " }{XPPEDIT 18 0 "x[02" "6#&%\"xG6#\"\"#" }{TEXT -1 10 " = 0.4 , " }{XPPEDIT 18 0 "x[03" "6#&%\"xG6#\"\"$" }{TEXT -1 10 " = \+ 0.6 , " }{XPPEDIT 18 0 "x[4]" "6#&%\"xG6#\"\"%" }{TEXT -1 12 " = 0.8 \+ y " }{XPPEDIT 18 0 "x[5]" "6#&%\"xG6#\"\"&" }{TEXT -1 7 " = 1. " }} {PARA 4 "" 0 "" {TEXT -1 63 "Tambi\351n dividimos [0,1] para y en \+ M subintervalos tomando" }}{PARA 4 "" 0 "" {TEXT -1 10 " k = " }{XPPEDIT 18 0 "(b-a)/M" "6#*&,&%\"bG\"\"\"%\"aG!\"\"F&%\"MGF(" } {TEXT -1 3 " = " }{XPPEDIT 18 0 "1/M" "6#*&\"\"\"F$%\"MG!\"\"" }{TEXT -1 33 " " }}{PARA 4 "" 0 "" {TEXT -1 7 "y luego" }}{PARA 4 "" 0 "" {TEXT -1 4 " " }{XPPEDIT 18 0 "y[m]" "6#&%\"yG6#%\"mG" }{TEXT -1 12 " = 0. + m h" }}{PARA 4 "" 0 "" {TEXT -1 5 "o sea" }}{PARA 4 "" 0 "" {TEXT -1 4 " " }{XPPEDIT 18 0 "y[0] " "6#&%\"yG6#\"\"!" }{TEXT -1 9 " = 0. , " }{XPPEDIT 18 0 "y[1]" "6#& %\"yG6#\"\"\"" }{TEXT -1 11 " = 0.25 , " }{XPPEDIT 18 0 "y[02" "6#&% \"yG6#\"\"#" }{TEXT -1 10 " = 0.5 , " }{XPPEDIT 18 0 "y[03" "6#&%\"yG 6#\"\"$" }{TEXT -1 14 " = 0.75 e " }{XPPEDIT 18 0 "y[4]" "6#&%\"yG 6#\"\"%" }{TEXT -1 7 " = 1. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "interface( labeling=false):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "Digits: =4:" }}}{EXCHG {PARA 256 "" 0 "" {TEXT 261 56 "La ecuaci\363n y la sol uci\363n exacta (conocida en este caso)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "findep:=(x,y)->0:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "gxeq0:=y->0.:gxeq1:=y->y:gyeq0:=x->0.:gyeq1:=x->x:" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "uexacta:=(x,y)->evalf(x*y) :" }}}{EXCHG {PARA 256 "" 0 "" {TEXT 257 9 "Los nodos" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "N:=5:h:=1/N:for n from 0 to N do x[ n]:=0+n*h; od;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"xG6#\"\"!F'" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"xG6#\"\"\"#F'\"\"&" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>&%\"xG6#\"\"##F'\"\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"xG6#\"\"$#F'\"\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"xG6#\"\"%#F'\"\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"xG6# \"\"&\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "M:=4:k:=1/M: for m from 0 to M do y[m]:=0+m*k; od;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"yG6#\"\"!F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"yG6#\"\"\" #F'\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"yG6#\"\"##\"\"\"F'" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"yG6#\"\"$#F'\"\"%" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>&%\"yG6#\"\"%\"\"\"" }}}{EXCHG {PARA 4 "" 0 "" {TEXT 258 24 "El orden de los nodos es" }}{PARA 4 "" 0 "" {TEXT 262 4 " " }{XPPEDIT 18 0 "P[l]" "6#&%\"PG6#%\"lG" }{TEXT 263 6 " = ( " } {XPPEDIT 18 0 "x[n]" "6#&%\"xG6#%\"nG" }{TEXT 264 3 " , " }{XPPEDIT 18 0 "y[m]" "6#&%\"yG6#%\"mG" }{TEXT 265 42 " ) para l = n + ( M - 1 - m ) ( N - 1 ) " }}{PARA 4 "" 0 "" {TEXT 266 14 "que va desde " } {XPPEDIT 18 0 "P[1] " "6#&%\"PG6#\"\"\"" }{TEXT 267 6 " = ( " } {XPPEDIT 18 0 "x[1]" "6#&%\"xG6#\"\"\"" }{TEXT 268 3 " , " }{XPPEDIT 18 0 "y[M-1]" "6#&%\"yG6#,&%\"MG\"\"\"F(!\"\"" }{TEXT 269 8 " ) = ( \+ " }{XPPEDIT 18 0 "x[1]" "6#&%\"xG6#\"\"\"" }{TEXT 270 3 " , " } {XPPEDIT 18 0 "y[3]" "6#&%\"yG6#\"\"$" }{TEXT 271 9 " ) hasta" }} {PARA 4 "" 0 "" {TEXT 281 4 " " }{XPPEDIT 18 0 "P[(N-1)*(M-1)] " "6 #&%\"PG6#*&,&%\"NG\"\"\"F)!\"\"F),&%\"MGF)F)F*F)" }{TEXT 273 3 " = " } {XPPEDIT 18 0 "P[12] " "6#&%\"PG6#\"#7" }{TEXT 278 7 " = ( " } {XPPEDIT 18 0 "x[N-1]" "6#&%\"xG6#,&%\"NG\"\"\"F(!\"\"" }{TEXT 274 3 " , " }{XPPEDIT 18 0 "y[1]" "6#&%\"yG6#\"\"\"" }{TEXT 275 8 " ) = ( " }{XPPEDIT 18 0 "x[4]" "6#&%\"xG6#\"\"%" }{TEXT 276 3 " , " }{XPPEDIT 18 0 "y[1]" "6#&%\"yG6#\"\"\"" }{TEXT 277 4 " ) " }}{PARA 4 "" 0 "" {TEXT 272 75 " La asignaci\363n inversa asigna l a ( n , m ) ponie ndo n como el resto" }}{PARA 4 "" 0 "" {TEXT 279 86 "m\341s 1 de \+ dividir l - 1 entre N - 1 (se observar\341 que esto es para que lo s restos" }}{PARA 4 "" 0 "" {TEXT 282 73 "efectivos vayan de 1 a N \+ - 1 Luego se calcula m restando l - n y " }}{PARA 4 "" 0 "" {TEXT 280 82 "dividi\351ndolo por N - 1 ; al resultado se le cambia d e signo y se le a\361ade M - 1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "L:=nm->nm[1]+(M-1-nm[2])*(N-1):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "P:=l->[(l-1) mod (N-1)+1,-(l-((l-1) mod (N-1) +1))/(N-1)+M-1]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "print(` El orden de los nodos es: `,seq(P(l),l=1..(N-1)*(M-1)));" }}{PARA 11 " " 1 "" {XPPMATH 20 "6/%;El~orden~de~los~nodos~es:~G7$\"\"\"\"\"$7$\"\" #F&7$F&F&7$\"\"%F&7$F%F(7$F(F(7$F&F(7$F+F(7$F%F%7$F(F%7$F&F%7$F+F%" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "numerar:=\{seq(u[P(l)[1],P( l)[2]]=u[l],l=1..(N-1)*(M-1))\};" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>% (numerarG<./&%\"uG6$\"\"\"\"\"$&F(6#F*/&F(6$\"\"#F+&F(6#F1/&F(6$F+F+&F (6#F+/&F(6$\"\"%F+&F(6#F " 0 " " {MPLTEXT 1 0 61 "inv_numerar:=\{seq(u[l]=u[P(l)[1],P(l)[2]],l=1..(N- 1)*(M-1))\};" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%,inv_numerarG<./&%\" uG6#\"\"\"&F(6$F*\"\"$/&F(6#\"\"#&F(6$F1F-/&F(6#F-&F(6$F-F-/&F(6#\"\"% &F(6$F " 0 "" {MPLTEXT 1 0 45 "for m from 0 to M do u[0,m] :=gxeq0(y[m]); od:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "for m from 0 to M do u[5,m]:=gxeq1(y[m]); od:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "for n from 0 to N do u[n,0]:=gyeq0(x[n]); od:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "for n from 0 to N do u[n,4]: =gyeq1(x[n]); od:" }}}{EXCHG {PARA 4 "" 0 "" {TEXT 260 89 "Ecuaciones; las variables en la forma u[n,m] y los valores de f en la forma \+ f[n,m] ," }}{PARA 4 "" 0 "" {TEXT 283 51 "aunque se ordenan por el ord en asignado con l(n.m)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 87 " for n from 1 to (N-1) do\nfor m from 1 to (M-1) do \nf[n,m]:=findep(x[ n],y[m]); \nod: \nod:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 205 "f or l from 1 to (N-1)*(M-1) do ecua(l):=evalf(2.*((h/k)^2+1)*u[P(l)[1], P(l)[2]]-(u[P(l)[1]+1,P(l)[2]]+u[P(l)[1]-1,P(l)[2]])-(h/k)^2*(u[P(l)[1 ],P(l)[2]+1]+u[P(l)[1],P(l)[2]-1])=-h^2*f[P(l)[1],P(l)[2]]); od;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>-%%ecuaG6#\"\"\"/,**&$\"%!G$!\"$F'&% \"uG6$F'\"\"$F'F'*&$F'\"\"!F'&F/6$\"\"#F1F'!\"\"$\"%!G\"!\"%F8*&$\"%+k F;F'&F/6$F'F7F'F8$F4F4" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%%ecuaG6# \"\"#/,,*&$\"%!G$!\"$\"\"\"&%\"uG6$F'\"\"$F.F.*&$F.\"\"!F.&F06$F2F2F.! \"\"*&$F.F5F.&F06$F.F2F.F8$\"%gD!\"%F8*&$\"%+kF?F.&F06$F'F'F.F8$F5F5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%%ecuaG6#\"\"$/,,*&$\"%!G$!\"$\"\" \"&%\"uG6$F'F'F.F.*&$F.\"\"!F.&F06$\"\"%F'F.!\"\"*&$F.F4F.&F06$\"\"#F' F.F8$\"%SQ!\"%F8*&$\"%+kF@F.&F06$F'F=F.F8$F4F4" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%%ecuaG6#\"\"%/,**&$\"%!G$!\"$\"\"\"&%\"uG6$F'\"\"$F. F.$\"%i7F-!\"\"*&$F.\"\"!F.&F06$F2F2F.F5*&$\"%+k!\"%F.&F06$F'\"\"#F.F5 $F8F8" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%%ecuaG6#\"\"&/,**&$\"%!G$! \"$\"\"\"&%\"uG6$F.\"\"#F.F.*&$F.\"\"!F.&F06$F2F2F.!\"\"*&$\"%+k!\"%F. &F06$F.\"\"$F.F8*&$F;F-%%ecuaG6#\"\"'/,,*&$\"%!G$!\"$\"\"\"&%\"uG6$\"\"#F2F. F.*&$F.\"\"!F.&F06$\"\"$F2F.!\"\"*&$F.F5F.&F06$F.F2F.F9*&$\"%+k!\"%F.& F06$F2F8F.F9*&$F@FAF.&F06$F2F.F.F9$F5F5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%%ecuaG6#\"\"(/,,*&$\"%!G$!\"$\"\"\"&%\"uG6$\"\"$\"\"#F.F.*&$F .\"\"!F.&F06$\"\"%F3F.!\"\"*&$F.F6F.&F06$F3F3F.F:*&$\"%+k!\"%F.&F06$F2 F2F.F:*&$FAFBF.&F06$F2F.F.F:$F6F6" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> -%%ecuaG6#\"\")/,,*&$\"%!G$!\"$\"\"\"&%\"uG6$\"\"%\"\"#F.F.$\"%+]!\"%! \"\"*&$F.\"\"!F.&F06$\"\"$F3F.F7*&$\"%+kF6F.&F06$F2F=F.F7*&$F@F6F.&F06 $F2F.F.F7$F:F:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%%ecuaG6#\"\"*/,(* &$\"%!G$!\"$\"\"\"&%\"uG6$F.F.F.F.*&$F.\"\"!F.&F06$\"\"#F.F.!\"\"*&$\" %+k!\"%F.&F06$F.F7F.F8$F4F4" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%%ecu aG6#\"#5/,**&$\"%!G$!\"$\"\"\"&%\"uG6$\"\"#F.F.F.*&$F.\"\"!F.&F06$\"\" $F.F.!\"\"*&$F.F5F.&F06$F.F.F.F9*&$\"%+k!\"%F.&F06$F2F2F.F9$F5F5" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>-%%ecuaG6#\"#6/,**&$\"%!G$!\"$\"\"\"& %\"uG6$\"\"$F.F.F.*&$F.\"\"!F.&F06$\"\"%F.F.!\"\"*&$F.F5F.&F06$\"\"#F. F.F9*&$\"%+k!\"%F.&F06$F2F>F.F9$F5F5" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#>-%%ecuaG6#\"#7/,**&$\"%!G$!\"$\"\"\"&%\"uG6$\"\"%F.F.F.$\"%+D!\"%! \"\"*&$F.\"\"!F.&F06$\"\"$F.F.F6*&$\"%+kF5F.&F06$F2\"\"#F.F6$F9F9" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "for l from 1 to (N-1)*(M-1) \+ do necua(l):=subs(numerar,ecua(l)); od;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%&necuaG6#\"\"\"/,**&$\"%!G$!\"$F'&%\"uGF&F'F'*&$F'\"\"!F'&F/6 #\"\"#F'!\"\"$\"%!G\"!\"%F6*&$\"%+kF9F'&F/6#\"\"&F'F6$F2F2" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%&necuaG6#\"\"#/,,*&$\"%!G$!\"$\"\"\"&%\"u GF&F.F.*&$F.\"\"!F.&F06#\"\"$F.!\"\"*&$F.F3F.&F06#F.F.F7$\"%gD!\"%F7*& $\"%+kF>F.&F06#\"\"'F.F7$F3F3" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%&n ecuaG6#\"\"$/,,*&$\"%!G$!\"$\"\"\"&%\"uGF&F.F.*&$F.\"\"!F.&F06#\"\"%F. !\"\"*&$F.F3F.&F06#\"\"#F.F7$\"%SQ!\"%F7*&$\"%+kF?F.&F06#\"\"(F.F7$F3F 3" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%&necuaG6#\"\"%/,**&$\"%!G$!\"$ \"\"\"&%\"uGF&F.F.$\"%i7F-!\"\"*&$F.\"\"!F.&F06#\"\"$F.F3*&$\"%+k!\"%F .&F06#\"\")F.F3$F6F6" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%&necuaG6#\" \"&/,**&$\"%!G$!\"$\"\"\"&%\"uGF&F.F.*&$F.\"\"!F.&F06#\"\"'F.!\"\"*&$ \"%+k!\"%F.&F06#F.F.F7*&$F:F;F.&F06#\"\"*F.F7$F3F3" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>-%&necuaG6#\"\"'/,,*&$\"%!G$!\"$\"\"\"&%\"uGF&F.F.*& $F.\"\"!F.&F06#\"\"(F.!\"\"*&$F.F3F.&F06#\"\"&F.F7*&$\"%+k!\"%F.&F06# \"\"#F.F7*&$F?F@F.&F06#\"#5F.F7$F3F3" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#>-%&necuaG6#\"\"(/,,*&$\"%!G$!\"$\"\"\"&%\"uGF&F.F.*&$F.\"\"!F.&F06# \"\")F.!\"\"*&$F.F3F.&F06#\"\"'F.F7*&$\"%+k!\"%F.&F06#\"\"$F.F7*&$F?F@ F.&F06#\"#6F.F7$F3F3" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%&necuaG6#\" \")/,,*&$\"%!G$!\"$\"\"\"&%\"uGF&F.F.$\"%+]!\"%!\"\"*&$F.\"\"!F.&F06# \"\"(F.F4*&$\"%+kF3F.&F06#\"\"%F.F4*&$F=F3F.&F06#\"#7F.F4$F7F7" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>-%&necuaG6#\"\"*/,(*&$\"%!G$!\"$\"\" \"&%\"uGF&F.F.*&$F.\"\"!F.&F06#\"#5F.!\"\"*&$\"%+k!\"%F.&F06#\"\"&F.F7 $F3F3" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%&necuaG6#\"#5/,**&$\"%!G$! \"$\"\"\"&%\"uGF&F.F.*&$F.\"\"!F.&F06#\"#6F.!\"\"*&$F.F3F.&F06#\"\"*F. F7*&$\"%+k!\"%F.&F06#\"\"'F.F7$F3F3" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #>-%&necuaG6#\"#6/,**&$\"%!G$!\"$\"\"\"&%\"uGF&F.F.*&$F.\"\"!F.&F06#\" #7F.!\"\"*&$F.F3F.&F06#\"#5F.F7*&$\"%+k!\"%F.&F06#\"\"(F.F7$F3F3" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>-%&necuaG6#\"#7/,**&$\"%!G$!\"$\"\"\" &%\"uGF&F.F.$\"%+D!\"%!\"\"*&$F.\"\"!F.&F06#\"#6F.F4*&$\"%+kF3F.&F06# \"\")F.F4$F7F7" }}}{EXCHG {PARA 4 "" 0 "" {TEXT 289 44 "Elementos no n ulos de la matriz del sistema " }}{PARA 4 "" 0 "" {TEXT -1 1 " " } {OLE 1 2179073 1 "[xm]Br=WfoRrB:::wk;nyyI;G:;:JKj:J:ZJJ;j:JyyyyyI<:nIf Y>j;ZJ:Q:T:ye;vy@jyX:wy;FdBJc\\:aD<^dBjd\\:gDfBB:=EZ:v:B:_Z:N;V;^;f;;JAjA >:[Z:F<^:N>V>^>f>n>v>>?F?N?V?^?f?n?v ?>`:B:];_;a;c;e;g;i;k;m;o;q;s;u;wK:vA>Be:jf<:oD:Ve:Jh<:uD:ne:ji<:;]:Ff:JkjkJljl JmjmJnjnJojoJpjpJqjqJrB:]=_=a=c=e=g=i=k=m=o=q=s=u=yE:fyyyY;^:NDYmq^H;k \\nGcMsFI>:::::::JEf:yyyxIF:>bs^lKnupvsKflxBjKGJMStB::>^dA[AWrRYs;V:>Z ;Z:j[vCWLdfBWZ:vYxY:B::::::F;nwp?<<:A=?R:E:yay=;Z:::::::^<>:F:AlqfG[maNFO=;::::::::_:C:yay=;Z:::: 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:::::::::::::::::::::::::::::::::::::::2:" }{TEXT -1 2 " " }}}{EXCHG {PARA 4 "" 0 "" {TEXT 288 55 "La soluci\363n num\351rica; recu\351rdes e que u[n,m] significa" }}{PARA 4 "" 0 "" {TEXT -1 21 " u ( x[n] \+ , y[m] )" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 80 "nsolucion:=solv e(\{seq(necua(l),l=1..(N-1)*(M-1))\},\{seq(u[l],l=1..(N-1)*(M-1))\}); " }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%*nsolucionG<./&%\"uG6#\"\"\"$\"% +:!\"%/&F(6#\"\"#$\"%+IF-/&F(6#\"\"$$\"%+XF-/&F(6#\"\"%$\"%+gF-/&F(6# \"\"&$\"%+5F-/&F(6#\"\"'$\"%+?F-/&F(6#\"\"(F2/&F(6#\"\")$\"%+SF-/&F(6# \"\"*$\"%+]!\"&/&F(6#\"#5FD/&F(6#\"#6F+/&F(6#\"#7FJ" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "solucion:=subs(inv_numerar,nsolucion);" } }{PARA 12 "" 1 "" {XPPMATH 20 "6#>%)solucionG<./&%\"uG6$\"\"\"\"\"$$\" %+:!\"%/&F(6$\"\"#F+$\"%+IF./&F(6$F+F+$\"%+XF./&F(6$\"\"%F+$\"%+gF./&F (6$F*F2$\"%+5F./&F(6$F2F2$\"%+?F./&F(6$F+F2F3/&F(6$F=F2$\"%+SF./&F(6$F *F*$\"%+]!\"&/&F(6$F2F*FC/&F(6$F+F*F,/&F(6$F=F*FH" }}}{EXCHG {PARA 4 " " 0 "" {TEXT 284 27 "En este caso, y como " }{XPPEDIT 18 0 "delt a^4 u/(delta x^4" "6#*(%&deltaG\"\"%%\"uG\"\"\"*&F$F'*$%\"xGF%F'!\"\" " }{TEXT -1 5 " = 0" }{TEXT 285 7 " y " }{TEXT -1 1 " " } {XPPEDIT 18 0 "delta^4 u/(delta y^4)" "6#*(%&deltaG\"\"%%\"uG\"\"\"* &F$F'*$%\"yGF%F'!\"\"" }{TEXT -1 5 " = 0" }{TEXT 286 37 " , el error \+ de truncaci\363n del m\351todo " }}{PARA 4 "" 0 "" {TEXT 287 47 "vale \+ ahora 0 , como comprobamos a continuaci\363n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "with(plottools):with(plots):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 103 "gcua:=pointplot3d([[0,1,0],[0,0,0],[1,0,0] ,[1,1,0],[0,1,0]],connect=true,color=\"DarkGray\",thickness=5):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "udom:=plot3d(0,x=0..l,t=0..0 .3,color=\"WhiteSmoke\"):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "verdadera:=plot3d(x*y, x=0..1, y=0..1):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 121 "puntos:=subs(solucion,textplot3d([seq(seq([0.2*i, 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