{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 32 "(13) Las Ecuaciones hiperb\363licas" }}{PARA 4 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 257 15 "Ejercicio 13-0 2" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT -1 28 "Para el problema hiperb\363lico" }}{PARA 4 "" 0 "" {TEXT -1 4 " " } {XPPEDIT 18 0 "delta^2 u/(delta t^2)" "6#*(%&deltaG\"\"#%\"uG\"\"\"* &F$F'*$%\"tGF%F'!\"\"" }{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'*$%\"xGF%F'!\"\"" }{TEXT -1 5 " = 0" }}{PARA 4 "" 0 "" {TEXT -1 18 " u ( x , 0 ) = " }{XPPEDIT 18 0 "f[1]" "6#&%\"fG6#\"\"\"" }{TEXT -1 11 " ( x ) , " }{XPPEDIT 18 0 "delta u/(delta t)" "6#*(%&deltaG\"\"\"%\"uGF%*&F$F%%\"tGF%!\" \"" }{TEXT -1 14 " ( x , 0 ) = " }{XPPEDIT 18 0 "f[2]" "6#&%\"fG6#\" \"#" }{TEXT -1 25 " ( x ) , " }}{PARA 4 "" 0 "" {TEXT -1 41 " u ( 0 , t ) = 0 y u ( l , t ) = 0 ," }}{PARA 4 "" 0 "" {TEXT -1 27 "con el ret\355culo habitual " }}{PARA 4 "" 0 "" {TEXT -1 7 " h = " }{XPPEDIT 18 0 "l/N" "6#*&%\"lG\"\"\"%\"NG!\"\"" } {TEXT -1 5 " , " }{XPPEDIT 18 0 "x[n]" "6#&%\"xG6#%\"nG" }{TEXT -1 11 " = n h , " }{XPPEDIT 18 0 "x[0]" "6#&%\"xG6#\"\"!" }{TEXT -1 4 " < " }{XPPEDIT 18 0 "x[1]" "6#&%\"xG6#\"\"\"" }{TEXT -1 11 " < ... < " }{XPPEDIT 18 0 "x[N]" "6#&%\"xG6#%\"NG" }{TEXT -1 24 " , \+ " }}{PARA 4 "" 0 "" {TEXT -1 15 " k > 0 , " } {XPPEDIT 18 0 "t[m]" "6#&%\"tG6#%\"mG" }{TEXT -1 10 " = m k , " } {XPPEDIT 18 0 "t[0]" "6#&%\"tG6#\"\"!" }{TEXT -1 4 " < " }{XPPEDIT 18 0 "t[1]" "6#&%\"tG6#\"\"\"" }{TEXT -1 4 " < " }{XPPEDIT 18 0 "t[2] " "6#&%\"tG6#\"\"#" }{TEXT -1 13 " < ... , " }}{PARA 4 "" 0 "" {TEXT -1 27 "se hacen las aproximaciones" }}{PARA 4 "" 0 "" {TEXT -1 10 " para " }{XPPEDIT 18 0 "delta^2 u/(delta t^2)" "6#*(%&deltaG \"\"#%\"uG\"\"\"*&F$F'*$%\"tGF%F'!\"\"" }{TEXT -1 20 " , f ' '(x) = " }{XPPEDIT 18 0 "(f(x+h)-2*f(x)+f(x-h))/(h^2)" "6#*&,(-%\"fG6#,&% \"xG\"\"\"%\"hGF*F**&\"\"#F*-F&6#F)F*!\"\"-F&6#,&F)F*F+F0F*F**$F+F-F0 " }{TEXT -1 8 " + O ( " }{XPPEDIT 18 0 "h^2" "6#*$%\"hG\"\"#" }{TEXT -1 55 " ) " }} {PARA 4 "" 0 "" {TEXT -1 10 " para " }{XPPEDIT 18 0 "delta^2 u/(d elta x^2)" "6#*(%&deltaG\"\"#%\"uG\"\"\"*&F$F'*$%\"xGF%F'!\"\"" } {TEXT -1 20 " , f ' '(x) = " }{XPPEDIT 18 0 "(-f(x+2h)+16f(x+h)- 30*f(x)+16f(x-h)-f(x-2h))/(12 h^2)" "6#*&,,-%\"fG6#,&%\"xG\"\"\"*&\"\" #F*%\"hGF*F*!\"\"*&\"#;F*-F&6#,&F)F*F-F*F*F**&\"#IF*-F&6#F)F*F.*&F0F*- F&6#,&F)F*F-F.F*F*-F&6#,&F)F**&F,F*F-F*F.F.F**&\"#7F**$F-F,F*F." } {TEXT -1 8 " + O ( " }{XPPEDIT 18 0 "h^4" "6#*$%\"hG\"\"%" }{TEXT -1 4 " ) " }}{PARA 4 "" 0 "" {TEXT -1 83 "Ded\372zcase el m\351todo en d iferencias que resulta, su orden, y descr\355base la mol\351cula " }} {PARA 4 "" 0 "" {TEXT -1 15 "computacional. " }}{PARA 4 "" 0 "" {TEXT -1 58 "Usando el m\351todo de FOURIER, b\372squese la condici\363n sob re " }{XPPEDIT 18 0 "lambda = (alpha k)/h" "6#/%'lambdaG*(%&alphaG\" \"\"%\"kGF'%\"hG!\"\"" }{TEXT -1 6 " para" }}{PARA 4 "" 0 "" {TEXT -1 44 "que el m\351todo sea estable. " }}}{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 }