{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 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 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 "T imes" 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 29 "(11) Las Ecuaciones el\355pticas" }}{PARA 4 " " 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 257 15 "Ejercicio 11-03" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT -1 25 "Para el problema el\355ptico" }}{PARA 4 "" 0 "" {TEXT -1 4 " " }{XPPEDIT 18 0 "delta^2 u/(delta x^2)" "6#*(%&deltaG\"\"#%\"uG\"\"\"*&F$F'*$% \"xGF%F'!\"\"" }{TEXT -1 6 " + " }{XPPEDIT 18 0 "delta^2 u/(delta \+ y^2)" "6#*(%&deltaG\"\"#%\"uG\"\"\"*&F$F'*$%\"yGF%F'!\"\"" }{TEXT -1 10 " = f(x,y)" }}{PARA 4 "" 0 "" {TEXT -1 69 "en el dominio [a,b]x[c ,d] , con una condici\363n de contorno adecuada, " }}{PARA 4 "" 0 "" {TEXT -1 26 "y con el ret\355culo habitual" }}{PARA 4 "" 0 "" {TEXT -1 4 " " }{XPPEDIT 18 0 "x[n]" "6#&%\"xG6#%\"nG" }{TEXT -1 18 " = a + h n, h = " }{XPPEDIT 18 0 "(b-a)/N" "6#*&,&%\"bG\"\"\"%\"aG!\"\"F &%\"NGF(" }{TEXT -1 3 " ," }}{PARA 4 "" 0 "" {TEXT -1 3 " " } {XPPEDIT 18 0 "y[m]" "6#&%\"yG6#%\"mG" }{TEXT -1 18 " = c + k m, k = " }{XPPEDIT 18 0 "(d-c)/M" "6#*&,&%\"dG\"\"\"%\"cG!\"\"F&%\"MGF(" } {TEXT -1 4 " , " }}{PARA 4 "" 0 "" {TEXT -1 94 "pero ahora supondremo s que, en este ret\355culo, h = k , lo que es esencial para lo que s igue. " }}{PARA 4 "" 0 "" {TEXT -1 22 "Se considera poniendo " } {XPPEDIT 18 0 "u[n m]" "6#&%\"uG6#*&%\"nG\"\"\"%\"mGF(" }{TEXT -1 6 " \+ = u( " }{XPPEDIT 18 0 "x[n]" "6#&%\"xG6#%\"nG" }{TEXT -1 4 " , " } {XPPEDIT 18 0 "y[m]" "6#&%\"yG6#%\"mG" }{TEXT -1 40 " ) el m\351todo \+ en diferencias, llamado de" }}{PARA 4 "" 0 "" {TEXT -1 22 "nueve punto s, dado por" }}{PARA 4 "" 0 "" {TEXT -1 5 " " }{XPPEDIT 18 0 "1/6; " "6#*&\"\"\"F$\"\"'!\"\"" }{TEXT -1 4 " ( " }{XPPEDIT 18 0 "u[n+1*m+ 1];" "6#&%\"uG6#,(%\"nG\"\"\"*&F(F(%\"mGF(F(F(F(" }{TEXT -1 3 " + " } {XPPEDIT 18 0 "u[n+1*m-1];" "6#&%\"uG6#,(%\"nG\"\"\"*&F(F(%\"mGF(F(F(! \"\"" }{TEXT -1 3 " + " }{XPPEDIT 18 0 "u[n-1*m+1];" "6#&%\"uG6#,(%\"n G\"\"\"*&F(F(%\"mGF(!\"\"F(F(" }{TEXT -1 3 " + " }{XPPEDIT 18 0 "u[n-1 *m-1];" "6#&%\"uG6#,(%\"nG\"\"\"*&F(F(%\"mGF(!\"\"F(F+" }{TEXT -1 5 " \+ ) + " }}{PARA 4 "" 0 "" {TEXT -1 7 " + " }{XPPEDIT 18 0 "2/3;" "6# *&\"\"#\"\"\"\"\"$!\"\"" }{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 3 " + " }{XPPEDIT 18 0 "u[n*m+1];" "6#&%\"uG6#,&*&%\"nG\"\" \"%\"mGF)F)F)F)" }{TEXT -1 3 " + " }{XPPEDIT 18 0 "u[n*m-1];" "6#&%\"u G6#,&*&%\"nG\"\"\"%\"mGF)F)F)!\"\"" }{TEXT -1 5 " ) - " }}{PARA 4 "" 0 "" {TEXT -1 7 " - " }{XPPEDIT 18 0 "10/3;" "6#*&\"#5\"\"\"\"\"$! \"\"" }{TEXT -1 2 " " }{XPPEDIT 18 0 "u[n*m];" "6#&%\"uG6#*&%\"nG\"\" \"%\"mGF(" }{TEXT -1 5 " = " }{XPPEDIT 18 0 "h^2/12;" "6#*&%\"hG\"\" #\"#7!\"\"" }{TEXT -1 3 " ( " }{XPPEDIT 18 0 "f[n+1*m];" "6#&%\"fG6#,& %\"nG\"\"\"*&F(F(%\"mGF(F(" }{TEXT -1 3 " + " }{XPPEDIT 18 0 "f[n-1*m] ;" "6#&%\"fG6#,&%\"nG\"\"\"*&F(F(%\"mGF(!\"\"" }{TEXT -1 3 " + " } {XPPEDIT 18 0 "f[n*m+1];" "6#&%\"fG6#,&*&%\"nG\"\"\"%\"mGF)F)F)F)" } {TEXT -1 3 " + " }{XPPEDIT 18 0 "f[n*m-1];" "6#&%\"fG6#,&*&%\"nG\"\"\" %\"mGF)F)F)!\"\"" }{TEXT -1 5 " + 8 " }{XPPEDIT 18 0 "f[n*m];" "6#&%\" fG6#*&%\"nG\"\"\"%\"mGF(" }{TEXT -1 3 " ) " }}{PARA 4 "" 0 "" {TEXT -1 88 "D\355gase qu\351 orden posee el error de truncaci\363n de dicho m\351todo en un ret\355culo en el que, " }}{PARA 4 "" 0 "" {TEXT -1 25 "como hemos dicho, h = k." }}}{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 }