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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 15 "Ejercicio 12-12
" }{TEXT 259 2 "  " }{TEXT 260 33 "(del EXAMEN ORDINARIO DE 09FEB09)" 
}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT -1 27 "Para el
 problema parab\363lico" }}{PARA 4 "" 0 "" {TEXT -1 4 "    " }
{XPPEDIT 18 0 "delta  u/(delta  t)" "6#*(%&deltaG\"\"\"%\"uGF%*&F$F%%
\"tGF%!\"\"" }{TEXT -1 5 "  -  " }{XPPEDIT 18 0 "alpha^2;" "6#*$%&alph
aG\"\"#" }{TEXT -1 3 "   " }{XPPEDIT 18 0 "delta^2  u/(delta  x^2)" "6
#*(%&deltaG\"\"#%\"uG\"\"\"*&F$F'*$%\"xGF%F'!\"\"" }{TEXT -1 13 "  = 0
 ,    x " }{XPPEDIT 18 0 "epsilon;" "6#%(epsilonG" }{TEXT -1 18 " [0,l
] ,  t >= 0 ," }}{PARA 4 "" 0 "" {TEXT -1 31 "    u ( x , 0 ) = f ( x \+
) ,    " }}{PARA 4 "" 0 "" {TEXT -1 105 "    u ( x , t ) = 0  , para t
odo x fuera de  (0,l) y todo  t >= 0  (esto es, la soluci\363n es id
\351nticamente" }}{PARA 4 "" 0 "" {TEXT -1 62 "                       \+
    nula en el exterior del dominio  x " }{XPPEDIT 18 0 "epsilon;" "6#
%(epsilonG" }{TEXT -1 18 " [0,l] ,  t >= 0 )" }}{PARA 4 "" 0 "" {TEXT 
-1 33 "se considera el ret\355culo habitual" }}{PARA 4 "" 0 "" {TEXT 
-1 4 "    " }{XPPEDIT 18 0 "x[n]" "6#&%\"xG6#%\"nG" }{TEXT -1 14 " = n
 h,   h = " }{XPPEDIT 18 0 "l/N;" "6#*&%\"lG\"\"\"%\"NG!\"\"" }{TEXT 
-1 3 "  ," }}{PARA 4 "" 0 "" {TEXT -1 3 "   " }{XPPEDIT 18 0 "t[m];" "
6#&%\"tG6#%\"mG" }{TEXT -1 8 " = m k, " }}{PARA 4 "" 0 "" {TEXT -1 86 
"Obt\351ngase el m\351todo en diferencias que proporcionan las aproxim
aciones a las derivadas" }}{PARA 4 "" 0 "" {TEXT -1 15 "    f ' (x) = \+
 " }{XPPEDIT 18 0 "(f(x+h)-f(x))/h;" "6#*&,&-%\"fG6#,&%\"xG\"\"\"%\"hG
F*F*-F&6#F)!\"\"F*F+F." }{TEXT -1 8 "  + O ( " }{XPPEDIT 18 0 "h;" "6#
%\"hG" }{TEXT -1 2 " )" }}{PARA 4 "" 0 "" {TEXT -1 7 " para  " }
{XPPEDIT 18 0 "delta u/(delta t)" "6#*(%&deltaG\"\"\"%\"uGF%*&F$F%%\"t
GF%!\"\"" }{TEXT -1 4 "  y " }}{PARA 4 "" 0 "" {TEXT -1 16 "    f ' '(
x) =  " }{XPPEDIT 18 0 "(f(x+2*h)-2*f(x)+f(x-2*h))/(4*h^2);" "6#*&,(-%
\"fG6#,&%\"xG\"\"\"*&\"\"#F*%\"hGF*F*F**&F,F*-F&6#F)F*!\"\"-F&6#,&F)F*
*&F,F*F-F*F1F*F**&\"\"%F**$F-F,F*F1" }{TEXT -1 8 "  + O ( " }{XPPEDIT 
18 0 "h^2" "6#*$%\"hG\"\"#" }{TEXT -1 3 " ) " }}{PARA 4 "" 0 "" {TEXT 
-1 6 "para  " }{XPPEDIT 18 0 "delta^2 u/(delta x^2)" "6#*(%&deltaG\"\"
#%\"uG\"\"\"*&F$F'*$%\"xGF%F'!\"\"" }{TEXT -1 63 "  . Ded\372zcase su \+
orden, la ecuaci\363n del m\351todo en t\351rminos de  " }{XPPEDIT 18 
0 "lambda = alpha^2*k/(h^2);" "6#/%'lambdaG*(%&alphaG\"\"#%\"kG\"\"\"*
$%\"hGF'!\"\"" }{TEXT -1 22 " , la forma matricial " }}{PARA 4 "" 0 "
" {TEXT -1 73 "del m\351todo y util\355cese el m\351todo de FOURIER pa
ra analizar su estabilidad." }}{PARA 4 "" 0 "" {TEXT -1 100 "Nota: Obs
\351rvese que, a la hora de aplicar el m\351todo para obtener las apro
ximaciones, ser\341 necesario " }}{PARA 4 "" 0 "" {TEXT -1 37 "hacer u
so de los valores auxiliares  " }{XPPEDIT 18 0 "u[-1,m];" "6#&%\"uG6$,
$\"\"\"!\"\"%\"mG" }{TEXT -1 5 "  y  " }{XPPEDIT 18 0 "u[N+1,m];" "6#&
%\"uG6$,&%\"NG\"\"\"F(F(%\"mG" }{TEXT -1 49 " , m=0,1,2,...  que se to
mar\341n nulos a partir de " }}{PARA 4 "" 0 "" {TEXT -1 61 "las condic
iones que verifica la soluci\363n de nuestro problema." }}}{EXCHG 
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