{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 "" -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 }{CSTYLE "" -1 259 "" 1 18 0 0 0 0 0 0 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 " Heading 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 }} {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 12-15 " }{TEXT 259 41 " (del EXAMEN EXTRAORDINARIO de 04JUL06)" }}{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 "del ta 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\351neas, considera mos los m\351todos " }}{PARA 4 "" 0 "" {TEXT -1 42 "'hacia 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\"\"\"%\"m GF+F+F+F+F+&F&6#*&F*F+F,F+!\"\"F+%\"kGF0" }{TEXT -1 4 " = " } {XPPEDIT 18 0 "alpha^2" "6#*$%&alphaG\"\"#" }{TEXT -1 1 " " }{XPPEDIT 18 0 "(u[n+1 m]-2*u[n m]+u[n-1 m])/h^2" "6#*&,(&%\"uG6#,&%\"nG\"\"\"*& F*F*%\"mGF*F*F**&\"\"#F*&F&6#*&F)F*F,F*F*!\"\"&F&6#,&F)F**&F*F*F,F*F2F *F**$%\"hGF.F2" }{TEXT -1 3 " " }}{PARA 4 "" 0 "" {TEXT -1 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#*$%&a lphaG\"\"#" }{TEXT -1 1 " " }{XPPEDIT 18 0 "(u[n+1 m]-2*u[n m]+u[n-1 m ])/h^2" "6#*&,(&%\"uG6#,&%\"nG\"\"\"*&F*F*%\"mGF*F*F**&\"\"#F*&F&6#*&F )F*F,F*F*!\"\"&F&6#,&F)F**&F*F*F,F*F2F*F**$%\"hGF.F2" }{TEXT -1 3 " \+ " }}{PARA 4 "" 0 "" {TEXT -1 68 "Se escribe el segundo para m+1 en l ugar de m , y se toma la media" }}{PARA 4 "" 0 "" {TEXT -1 67 "aritm \351tica de ambos, pero con coeficientes -1 y 2 , obteni\351ndose" }}{PARA 4 "" 0 "" {TEXT -1 31 "as\355 un m\351todo mezcla de ambos ." }}{PARA 4 "" 0 "" {TEXT -1 67 "Construir matricialmente dicho m\351tod o y estudiar la estabilidad del" }}{PARA 4 "" 0 "" {TEXT -1 44 "m\351t odo, empleando el procedimiento matricial" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "interface(labeling=false):" }}}}{MARK "0 3 0" 15 }{VIEWOPTS 1 1 0 3 4 1802 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }