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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 12-11
" }{TEXT 259 1 " " }{TEXT 260 34 " (del EXAMEN ORDINARIO DE 09FEB10)" 
}}{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$F%%
\"tGF%!\"\"" }{TEXT -1 4 "  - " }{XPPEDIT 18 0 "alpha^2" "6#*$%&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 57 "con condiciones de contorno homog\351
neas, y denotando por  " }{XPPEDIT 18 0 "lambda;" "6#%'lambdaG" }
{TEXT -1 14 "  la cantidad " }}{PARA 4 "" 0 "" {XPPEDIT 18 0 "lambda" 
"6#%'lambdaG" }{TEXT -1 3 " = " }{XPPEDIT 18 0 "alpha^2*k/(h^2);" "6#*
(%&alphaG\"\"#%\"kG\"\"\"*$%\"hGF%!\"\"" }{TEXT -1 41 " , nos presenta
n el m\351todo en diferencias" }}{PARA 4 "" 0 "" {TEXT -1 4 "    " }
{XPPEDIT 18 0 "u[n*m+2];" "6#&%\"uG6#,&*&%\"nG\"\"\"%\"mGF)F)\"\"#F)" 
}{TEXT -1 5 " - 4 " }{XPPEDIT 18 0 "u[n*m+1];" "6#&%\"uG6#,&*&%\"nG\"
\"\"%\"mGF)F)F)F)" }{TEXT -1 6 " = (4 " }{XPPEDIT 18 0 "lambda;" "6#%'
lambdaG" }{TEXT -1 6 " - 3) " }{XPPEDIT 18 0 "u[n m]" "6#&%\"uG6#*&%\"
nG\"\"\"%\"mGF(" }{TEXT -1 5 " - 2 " }{XPPEDIT 18 0 "lambda" "6#%'lamb
daG" }{TEXT -1 4 "  ( " }{XPPEDIT 18 0 "u[n+1*m];" "6#&%\"uG6#,&%\"nG
\"\"\"*&F(F(%\"mGF(F(" }{TEXT -1 3 " + " }{XPPEDIT 18 0 "u[n-1 m]" "6#
&%\"uG6#,&%\"nG\"\"\"*&F(F(%\"mGF(!\"\"" }{TEXT -1 4 " )  " }}{PARA 4 
"" 0 "" {TEXT -1 26 "donde las aproximaciones  " }{XPPEDIT 18 0 "u[n*m
];" "6#&%\"uG6#*&%\"nG\"\"\"%\"mGF(" }{TEXT -1 4 " =  " }{XPPEDIT 18 
0 "u(x[n],t[m]);" "6#-%\"uG6$&%\"xG6#%\"nG&%\"tG6#%\"mG" }{TEXT -1 29 
"  tienen el sentido habitual." }}{PARA 4 "" 0 "" {TEXT -1 69 "Calc
\372lese el orden de truncaci\363n del m\351todo. Est\372diese la esta
bilidad" }}{PARA 4 "" 0 "" {TEXT -1 55 "del m\351todo por alguno de lo
s procedimientos habituales." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
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