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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 12-07
" }}{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$F%%
\"tGF%!\"\"" }{TEXT -1 5 "  -  " }{XPPEDIT 18 0 "delta^2  u/(delta  x^
2)" "6#*(%&deltaG\"\"#%\"uG\"\"\"*&F$F'*$%\"xGF%F'!\"\"" }{TEXT -1 5 "
  = 0" }}{PARA 4 "" 0 "" {TEXT -1 32 "    u ( x , 0 ) = f ( x ) .     \+
" }}{PARA 4 "" 0 "" {TEXT -1 41 "    u ( 0 , t ) = 0  y  u ( l , t ) =
 0 ," }}{PARA 4 "" 0 "" {TEXT -1 86 "con condiciones de contorno homog
\351neas, se considera el ret\355culo habitual y el m\351todo " }}
{PARA 4 "" 0 "" {TEXT -1 43 "en diferencias, llamado m\351todo de DOUG
LAS, " }}{PARA 4 "" 0 "" {TEXT -1 11 "    (1 - 6 " }{XPPEDIT 18 0 "lam
bda;" "6#%'lambdaG" }{TEXT -1 3 " ) " }{XPPEDIT 18 0 "u[n-1*m+1];" "6#
&%\"uG6#,(%\"nG\"\"\"*&F(F(%\"mGF(!\"\"F(F(" }{TEXT -1 12 " + (10 + 12
 " }{XPPEDIT 18 0 "lambda;" "6#%'lambdaG" }{TEXT -1 3 " ) " }{XPPEDIT 
18 0 "u[n*m+1];" "6#&%\"uG6#,&*&%\"nG\"\"\"%\"mGF)F)F)F)" }{TEXT -1 
10 " + (1 - 6 " }{XPPEDIT 18 0 "lambda;" "6#%'lambdaG" }{TEXT -1 3 " )
 " }{XPPEDIT 18 0 "u[n+1*m+1];" "6#&%\"uG6#,(%\"nG\"\"\"*&F(F(%\"mGF(F
(F(F(" }{TEXT -1 2 " =" }}{PARA 4 "" 0 "" {TEXT -1 14 "     = (1 + 6 \+
" }{XPPEDIT 18 0 "lambda;" "6#%'lambdaG" }{TEXT -1 3 " ) " }{XPPEDIT 
18 0 "u[n-1*m];" "6#&%\"uG6#,&%\"nG\"\"\"*&F(F(%\"mGF(!\"\"" }{TEXT 
-1 12 " + (10 - 12 " }{XPPEDIT 18 0 "lambda;" "6#%'lambdaG" }{TEXT -1 
3 " ) " }{XPPEDIT 18 0 "u[n*m];" "6#&%\"uG6#*&%\"nG\"\"\"%\"mGF(" }
{TEXT -1 10 " + (1 + 6 " }{XPPEDIT 18 0 "lambda;" "6#%'lambdaG" }
{TEXT -1 3 " ) " }{XPPEDIT 18 0 "u[n+1*m];" "6#&%\"uG6#,&%\"nG\"\"\"*&
F(F(%\"mGF(F(" }{TEXT -1 2 "  " }}{PARA 4 "" 0 "" {TEXT -1 5 "con  " }
{XPPEDIT 18 0 "lambda" "6#%'lambdaG" }{TEXT -1 3 " = " }{XPPEDIT 18 0 
"k/(h^2);" "6#*&%\"kG\"\"\"*$%\"hG\"\"#!\"\"" }{TEXT -1 31 " y las not
aciones habituales.  " }}{PARA 4 "" 0 "" {TEXT -1 77 "a) Descr\355base
 la forma matricial del m\351todo en t\351rminos de la habitual matriz
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT -1 35 "     \+
    |   2  -1   0   . . .    |" }}{PARA 4 "" 0 "" {TEXT -1 35 "       \+
  |  -1   2  -1   . . .    |" }}{PARA 4 "" 0 "" {TEXT -1 33 "   B = | \+
  0  -1   2   . . .    |" }}{PARA 4 "" 0 "" {TEXT -1 37 "         |   \+
.    .    .            |" }}{PARA 4 "" 0 "" {TEXT -1 38 "         |   \+
.    .    .            | " }}{PARA 4 "" 0 "" {TEXT -1 21 "cuyoa autova
lores son" }}{PARA 4 "" 0 "" {TEXT -1 3 "   " }{XPPEDIT 18 0 "rho[n];
" "6#&%$rhoG6#%\"nG" }{TEXT -1 12 " = 4 ( sen  " }{XPPEDIT 18 0 "n pi/
(2 N)" "6#*(%\"nG\"\"\"%#piGF%*&\"\"#F%%\"NGF%!\"\"" }{TEXT -1 54 "  )
 ^2 ,   n = 1 , ... , N - 1 , para los autovectores" }}{PARA 4 "" 0 "
" {TEXT -1 4 "    " }{XPPEDIT 18 0 "x^([n])" "6#)%\"xG7#%\"nG" }{TEXT 
-1 10 "  = ( sen " }{XPPEDIT 18 0 "n pi/N" "6#*(%\"nG\"\"\"%#piGF%%\"N
G!\"\"" }{TEXT -1 9 "  ,  sen " }{XPPEDIT 18 0 "2 n pi/N" "6#**\"\"#\"
\"\"%\"nGF%%#piGF%%\"NG!\"\"" }{TEXT -1 14 "  , ... , sen " }{XPPEDIT 
18 0 " ( N-1)*n pi)/(N)" "6#**,&%\"NG\"\"\"F&!\"\"F&%\"nGF&%#piGF&F%F'
" }{TEXT -1 29 "   ) ,   n = 1 , ... , N - 1 " }}{PARA 4 "" 0 "" 
{TEXT -1 90 "b) Calc\372lense los autovalores que aparecen en el estud
io, por el procedimiento matricial, " }}{PARA 4 "" 0 "" {TEXT -1 32 "d
e la estabilidad de este m\351todo" }}{PARA 4 "" 0 "" {TEXT -1 76 "c) \+
Pru\351bese usando dicho procedimiento matricial que el m\351todo de D
OUGLAS es" }}{PARA 4 "" 0 "" {TEXT -1 26 "incondicionalmente estable" 
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