{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 }{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 12-06 " }}{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 67 "vamos a considerar el m\351todo de l as 'diferencias hacia adelante' " }}{PARA 4 "" 0 "" {TEXT -1 8 "dado \+ por" }}{PARA 4 "" 0 "" {TEXT -1 4 " " }{XPPEDIT 18 0 "u[n m+1]" "6# &%\"uG6#,&*&%\"nG\"\"\"%\"mGF)F)F)F)" }{TEXT -1 12 " = ( 1 - 2 " } {XPPEDIT 18 0 "lambda" "6#%'lambdaG" }{TEXT -1 4 " ) " }{XPPEDIT 18 0 "u[n m]" "6#&%\"uG6#*&%\"nG\"\"\"%\"mGF(" }{TEXT -1 4 " + " } {XPPEDIT 18 0 "lambda" "6#%'lambdaG" }{TEXT -1 4 " ( " }{XPPEDIT 18 0 "u[n+1 m]" "6#&%\"uG6#,&%\"nG\"\"\"*&F(F(%\"mGF(F(" }{TEXT -1 3 " + \+ " }{XPPEDIT 18 0 "u[n-1 m]" "6#&%\"uG6#,&%\"nG\"\"\"*&F(F(%\"mGF(!\"\" " }{TEXT -1 6 " ) " }}{PARA 4 "" 0 "" {TEXT -1 6 "con " } {XPPEDIT 18 0 "\\lambda" "6#%'lambdaG" }{TEXT -1 4 " = " }{XPPEDIT 18 0 "alpha^2 k/h^2" "6#*(%&alphaG\"\"#%\"kG\"\"\"*$%\"hGF%!\"\"" } {TEXT -1 15 " , o poniendo" }}{PARA 4 "" 0 "" {TEXT -1 4 " " } {XPPEDIT 18 0 "u^[k]" "6#)%\"uG7#%\"kG" }{TEXT -1 6 " = ( " } {XPPEDIT 18 0 "u[1 k]" "6#&%\"uG6#*&\"\"\"F'%\"kGF'" }{TEXT -1 4 " , \+ " }{XPPEDIT 18 0 "u[2 k]" "6#&%\"uG6#*&\"\"#\"\"\"%\"kGF(" }{TEXT -1 10 " , ... , " }{XPPEDIT 18 0 "u[N-1 k]" "6#&%\"uG6#,&%\"NG\"\"\"*&F( F(%\"kGF(!\"\"" }{TEXT -1 7 " ) " }}{PARA 4 "" 0 "" {TEXT -1 34 " \+ | 1 - 2 " }{XPPEDIT 18 0 "lambda" "6#%'lambda G" }{TEXT -1 8 " " }{XPPEDIT 18 0 "lambda" "6#%'lambdaG" } {TEXT -1 26 " 0 . . . |" }}{PARA 4 "" 0 "" {TEXT -1 33 " | " }{XPPEDIT 18 0 "lambda" "6#%'la mbdaG" }{TEXT -1 12 " 1 - 2 " }{XPPEDIT 18 0 "lambda" "6#%'lambda G" }{TEXT -1 8 " " }{XPPEDIT 18 0 "lambda" "6#%'lambdaG" } {TEXT -1 14 " . . . |" }}{PARA 4 "" 0 "" {TEXT -1 11 " A = I - " }{XPPEDIT 18 0 "lambda" "6#%'lambdaG" }{TEXT -1 26 " B = | 0 " }{XPPEDIT 18 0 "lambda" "6#%'lambdaG" }{TEXT -1 12 " \+ 1 - 2 " }{XPPEDIT 18 0 "lambda" "6#%'lambdaG" }{TEXT -1 12 " . . . \+ |" }}{PARA 4 "" 0 "" {TEXT -1 76 " | . . . |" }}{PARA 4 "" 0 "" {TEXT -1 77 " | . . . \+ | " }}{PARA 4 "" 0 "" {TEXT -1 23 "en forma matricial, por " }}{PARA 4 "" 0 "" {TEXT -1 6 " " }{XPPEDIT 18 0 "u^[m+1]" "6#)% \"uG7#,&%\"mG\"\"\"F(F(" }{TEXT -1 8 " = A " }{XPPEDIT 18 0 "u^[m] " "6#)%\"uG7#%\"mG" }{TEXT -1 22 " " }}{PARA 4 " " 0 "" {TEXT -1 51 "Se recuerda que una condici\363n suficiente para q ue " }{XPPEDIT 18 0 "rho" "6#%$rhoG" }{TEXT -1 24 " ( A ) <= 1 (lo \+ que es" }}{PARA 4 "" 0 "" {TEXT -1 49 "una condici\363n suficiente de \+ estabilidad) es que " }{XPPEDIT 18 0 "lambda" "6#%'lambdaG" }{TEXT -1 5 " <= " }{XPPEDIT 18 0 "1/2" "6#*&\"\"\"F$\"\"#!\"\"" }{TEXT -1 6 " " }}{PARA 4 "" 0 "" {TEXT -1 78 "\332sese el m\351todo de FOU RIER para buscar una condici\363n necesaria de estabilidad." }}} {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 }