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{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
4" }{TEXT 259 35 "  (del EXAMEN ORDINARIO de 09FEB04)" }}{PARA 0 "" 0 
"" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT -1 28 "Para el problema hiper
b\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 6 "  -   " }{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$F%%\"tGF%!\"\"" }{TEXT 
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-1 25 " ( x ) ,                 " }}{PARA 4 "" 0 "" {TEXT -1 41 "    u
 ( 0 , t ) = 0  y  u ( l , t ) = 0 ," }}{PARA 4 "" 0 "" {TEXT -1 27 "s
e considera un ret\355culo   " }}{PARA 4 "" 0 "" {TEXT -1 7 "   h = " 
}{XPPEDIT 18 0 "l/N" "6#*&%\"lG\"\"\"%\"NG!\"\"" }{TEXT -1 5 "  ,  " }
{XPPEDIT 18 0 "x[n]" "6#&%\"xG6#%\"nG" }{TEXT -1 11 " = n h  ,  " }
{XPPEDIT 18 0 "x[0]" "6#&%\"xG6#\"\"!" }{TEXT -1 4 " <  " }{XPPEDIT 
18 0 "x[1]" "6#&%\"xG6#\"\"\"" }{TEXT -1 11 " <  ... <  " }{XPPEDIT 
18 0 "x[N]" "6#&%\"xG6#%\"NG" }{TEXT -1 24 "  ,                     " 
}}{PARA 4 "" 0 "" {TEXT -1 15 "   k = h    ,  " }{XPPEDIT 18 0 "t[m]" 
"6#&%\"tG6#%\"mG" }{TEXT -1 16 " = m k = m h ,  " }{XPPEDIT 18 0 "t[0]
" "6#&%\"tG6#\"\"!" }{TEXT -1 4 " <  " }{XPPEDIT 18 0 "t[1]" "6#&%\"tG
6#\"\"\"" }{TEXT -1 4 " <  " }{XPPEDIT 18 0 "t[2]" "6#&%\"tG6#\"\"#" }
{TEXT -1 13 "  < ...  ,   " }}{PARA 4 "" 0 "" {TEXT -1 81 "donde se ut
iliza el mismo incremento para  x  y para  t . Para crear un m\351todo
 en" }}{PARA 4 "" 0 "" {TEXT -1 69 "diferencias se aproximan ambas der
ivadas segundas mediante la f\363rmula" }}{PARA 4 "" 0 "" {TEXT -1 17 
"     f ' '(x) =  " }{XPPEDIT 18 0 "(f(x+h)-2*f(x)+f(x-h))/(h^2)" "6#*
&,(-%\"fG6#,&%\"xG\"\"\"%\"hGF*F**&\"\"#F*-F&6#F)F*!\"\"-F&6#,&F)F*F+F
0F*F**$F+F-F0" }{TEXT -1 8 "  + O ( " }{XPPEDIT 18 0 "h^2" "6#*$%\"hG
\"\"#" }{TEXT -1 55 " )                                               \+
      " }}{PARA 4 "" 0 "" {TEXT -1 80 "D\355gase qu\351 ecuaci\363n en
 diferencias resulta, descr\355base la mol\351cula computacional" }}
{PARA 4 "" 0 "" {TEXT -1 78 "y escr\355base el m\351todo en forma matr
icial. Finalmente, disc\372tase la estabilidad" }}{PARA 4 "" 0 "" 
{TEXT -1 62 "del m\351todo empleando alguno de los procedimientos habi
tuales. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}
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