{VERSION 5 0 "IBM INTEL NT" "5.0" } {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 "" -1 256 "" 1 24 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE " " -1 257 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 258 "" 1 24 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 2 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 50 0 0 0 0 1 0 0 0 0 0 0 0 1 }1 0 0 0 6 6 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 2" 3 4 1 {CSTYLE "" -1 -1 "" 1 14 0 0 255 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 4 4 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 4 "" 0 "" {TEXT 256 14 "Ejercicios de " }}{PARA 4 "" 0 "" {TEXT 258 31 "(12) Las Ecuaciones parab\363licas" }}{PARA 4 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 257 15 "Ejercicio 12-03 " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT -1 27 "Para \+ el problema parab\363lico" }}{PARA 4 "" 0 "" {TEXT -1 4 " " } {XPPEDIT 18 0 "delta u/(delta t)" "6#*(%&deltaG\"\"\"%\"uGF%*&F$F%% \"tGF%!\"\"" }{TEXT -1 4 " - " }{XPPEDIT 18 0 "alpha^2" "6#*$%&alphaG \"\"#" }{TEXT -1 2 " " }{XPPEDIT 18 0 "delta^2 u/(delta x^2)" "6#*( %&deltaG\"\"#%\"uG\"\"\"*&F$F'*$%\"xGF%F'!\"\"" }{TEXT -1 5 " = 0" }} {PARA 4 "" 0 "" {TEXT -1 32 " u ( x , 0 ) = f ( x ) . " }} {PARA 4 "" 0 "" {TEXT -1 41 " u ( 0 , t ) = 0 y u ( l , t ) = 0 , " }}{PARA 4 "" 0 "" {TEXT -1 66 "con condiciones de contorno homog\351 neas, consideramos los m\351todos " }}{PARA 4 "" 0 "" {TEXT -1 42 "'h acia adelante' y 'hacia atr\341s' dados por" }}{PARA 4 "" 0 "" {TEXT -1 4 " " }{XPPEDIT 18 0 "(u[n m+1]-u[n m])/k" "6#*&,&&%\"uG6#,&*&% \"nG\"\"\"%\"mGF+F+F+F+F+&F&6#*&F*F+F,F+!\"\"F+%\"kGF0" }{TEXT -1 4 " \+ = " }{XPPEDIT 18 0 "alpha^2" "6#*$%&alphaG\"\"#" }{TEXT -1 1 " " } {XPPEDIT 18 0 "(u[n+1 m]-2*u[n m]+u[n-1 m])/h^2" "6#*&,(&%\"uG6#,&%\"n G\"\"\"*&F*F*%\"mGF*F*F**&\"\"#F*&F&6#*&F)F*F,F*F*!\"\"&F&6#,&F)F**&F* F*F,F*F2F*F**$%\"hGF.F2" }{TEXT -1 3 " " }}{PARA 4 "" 0 "" {TEXT -1 82 "y \+ " }}{PARA 4 "" 0 "" {TEXT -1 4 " " }{XPPEDIT 18 0 " (u[n m]-u[n m-1])/k" "6#*&,&&%\"uG6#*&%\"nG\"\"\"%\"mGF*F*&F&6#,&*&F)F *F+F*F*F*!\"\"F0F*%\"kGF0" }{TEXT -1 4 " = " }{XPPEDIT 18 0 "alpha^2 " "6#*$%&alphaG\"\"#" }{TEXT -1 1 " " }{XPPEDIT 18 0 "(u[n+1 m]-2*u[n \+ m]+u[n-1 m])/h^2" "6#*&,(&%\"uG6#,&%\"nG\"\"\"*&F*F*%\"mGF*F*F**&\"\"# F*&F&6#*&F)F*F,F*F*!\"\"&F&6#,&F)F**&F*F*F,F*F2F*F**$%\"hGF.F2" } {TEXT -1 3 " " }}{PARA 4 "" 0 "" {TEXT -1 68 "Se escribe el segundo \+ para m+1 en lugar de m , y se toma la media" }}{PARA 4 "" 0 "" {TEXT -1 62 "aritm\351tica de ambos. Esto nos da el m\351todo de CRANK -NICOLSON ." }}{PARA 4 "" 0 "" {TEXT -1 64 "Construir matricialmente d icho m\351todo y comprobar que es estable" }}{PARA 4 "" 0 "" {TEXT -1 65 "con independencia de las relaciones entre h y k , incrementos \+ " }}{PARA 4 "" 0 "" {TEXT -1 16 "en x y en t ." }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "interface(labeling=false):" }}}}{MARK "0 0 0" 0 } {VIEWOPTS 1 1 0 3 4 1802 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }