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{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 50 "Ejercicio 12-20 \+
 (del EXAMEN ORDINARIO de 01FEB06)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 4 "" 0 "" {TEXT -1 48 "Para el problema dado por la ecuaci\363n \+
parab\363lica" }}{PARA 4 "" 0 "" {TEXT -1 4 "    " }{XPPEDIT 18 0 "del
ta  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 71 "con condiciones de contorno homog\351neas, se tiene \+
el siguiente  m\351todo  " }}{PARA 4 "" 0 "" {TEXT -1 3 "   " }
{XPPEDIT 18 0 "(u[n*m+1]-u[n*m-1])/(2*k);" "6#*&,&&%\"uG6#,&*&%\"nG\"
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{TEXT -1 3 "   " }{XPPEDIT 18 0 "-alpha^2;" "6#,$*$%&alphaG\"\"#!\"\"
" }{TEXT -1 2 "  " }{XPPEDIT 18 0 "(u[n+1*m]-(u[n*m+1]+u[n*m-1])+u[n-1
*m])/(h^2);" "6#*&,(&%\"uG6#,&%\"nG\"\"\"*&F*F*%\"mGF*F*F*,&&F&6#,&*&F
)F*F,F*F*F*F*F*&F&6#,&*&F)F*F,F*F*F*!\"\"F*F6&F&6#,&F)F**&F*F*F,F*F6F*
F**$%\"hG\"\"#F6" }{TEXT -1 7 "  = 0  " }}{PARA 4 "" 0 "" {TEXT -1 45 
"conocido como 'esquema de DU FORT - FRANKEL'." }}{PARA 4 "" 0 "" 
{TEXT -1 32 "Establ\351zcase la ecuaci\363n sobre  " }{XPPEDIT 18 0 "l
ambda;" "6#%'lambdaG" }{TEXT -1 3 " = " }{XPPEDIT 18 0 "alpha^2;" "6#*
$%&alphaG\"\"#" }{TEXT -1 1 " " }{TEXT 259 1 "k" }{TEXT -1 3 " / " }
{XPPEDIT 18 0 "h^2;" "6#*$%\"hG\"\"#" }{TEXT -1 23 " , b  y  d que pla
ntea " }}{PARA 4 "" 0 "" {TEXT -1 54 "el m\351todo de FOURIER cuando s
e aplica este esquema a  " }{XPPEDIT 18 0 "exp(i*n*b*h)*exp(m*d*k);" "
6#*&-%$expG6#**%\"iG\"\"\"%\"nGF)%\"bGF)%\"hGF)F)-F%6#*(%\"mGF)%\"dGF)
%\"kGF)F)" }{TEXT -1 3 "   " }}{PARA 4 "" 0 "" {TEXT -1 63 "Comprobar \+
que, en cualquiera de los casos, siempre se tiene que" }}{PARA 4 "" 0 
"" {TEXT -1 5 "   | " }{XPPEDIT 18 0 "exp(d*k);" "6#-%$expG6#*&%\"dG\"
\"\"%\"kGF(" }{TEXT -1 9 " |  <= 1 " }}{PARA 4 "" 0 "" {TEXT -1 56 "Qu
\351 significa esto de cara a la estabilidad del esquema." }}}{EXCHG 
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