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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 12 "Ejercicio 13" 
}{TEXT 259 39 "-05   (del EXAMEN ORDINARIO de 04FEB08)" }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT -1 28 "Para el problema hip
erb\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 apro
ximaciones" }}{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&
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{XPPEDIT 18 0 "h^2" "6#*$%\"hG\"\"#" }{TEXT -1 55 " )                 \+
                                    " }}{PARA 4 "" 0 "" {TEXT -1 10 " \+
  para   " }{XPPEDIT 18 0 "delta^2  u/(delta  x^2)" "6#*(%&deltaG\"\"#
%\"uG\"\"\"*&F$F'*$%\"xGF%F'!\"\"" }{TEXT -1 20 "  ,     f ' '(x) =  \+
" }{XPPEDIT 18 0 "(-f(x+2*h)+6*f(x+h)-10*f(x)+6*f(x-h)-f(x-2*h))/(2*h^
2);" "6#*&,,-%\"fG6#,&%\"xG\"\"\"*&\"\"#F*%\"hGF*F*!\"\"*&\"\"'F*-F&6#
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0 "h^2;" "6#*$%\"hG\"\"#" }{TEXT -1 4 " )  " }}{PARA 4 "" 0 "" {TEXT 
-1 83 "Ded\372zcase el m\351todo en diferencias que resulta, su orden,
 y descr\355base la mol\351cula " }}{PARA 4 "" 0 "" {TEXT -1 15 "compu
tacional. " }}{PARA 4 "" 0 "" {TEXT -1 57 "Adem\341s, d\355gase lo que
 afirma el m\351todo de FOURIER sobre  " }{XPPEDIT 18 0 "lambda = (alp
ha k)/h" "6#/%'lambdaG*(%&alphaG\"\"\"%\"kGF'%\"hG!\"\"" }{TEXT -1 9 "
  cuando " }}{PARA 4 "" 0 "" {TEXT -1 55 "se analiza la estabilidad de
l m\351todo.                  " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
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