{VERSION 6 0 "IBM INTEL NT" "6.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 236 0 76 0 0 0 2 0 0 
0 0 0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 48 37 0 0 0 0 0 0 0 0 0 0 
0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 }
{CSTYLE "" -1 256 "" 1 24 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 
257 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 258 "" 1 24 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 259 "" 1 18 0 0 0 0 0 0 0 0 
0 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 2 0 
0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading
 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 50 0 0 0 0 1 0 0 0 0 0 0 0 1 }1 0 
0 0 6 6 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 2" 3 4 1 {CSTYLE "" -1 -1 "
" 1 14 0 0 255 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 4 4 0 0 0 0 0 0 -1 0 }
{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 11 12 1 
{CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 
0 0 0 0 0 -1 0 }}
{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 12-16
" }{TEXT 259 41 "   (del EXAMEN EXTRAORDINARIO de 09JUL03)" }}{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 "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 66 "con condiciones de contorno homog\351neas, considera
mos los  m\351todos " }}{PARA 4 "" 0 "" {TEXT -1 42 "'hacia adelante' \+
y 'hacia atr\341s' dados por" }}{PARA 4 "" 0 "" {TEXT -1 4 "    " }
{XPPEDIT 18 0 "(u[n m+1]-u[n m])/k" "6#*&,&&%\"uG6#,&*&%\"nG\"\"\"%\"m
GF+F+F+F+F+&F&6#*&F*F+F,F+!\"\"F+%\"kGF0" }{TEXT -1 4 "  = " }
{XPPEDIT 18 0 "alpha^2" "6#*$%&alphaG\"\"#" }{TEXT -1 1 " " }{XPPEDIT 
18 0 "(u[n+1 m]-2*u[n m]+u[n-1 m])/h^2" "6#*&,(&%\"uG6#,&%\"nG\"\"\"*&
F*F*%\"mGF*F*F**&\"\"#F*&F&6#*&F)F*F,F*F*!\"\"&F&6#,&F)F**&F*F*F,F*F2F
*F**$%\"hGF.F2" }{TEXT -1 3 "   " }}{PARA 4 "" 0 "" {TEXT -1 82 "y    \+
                                                                      \+
       " }}{PARA 4 "" 0 "" {TEXT -1 4 "    " }{XPPEDIT 18 0 "(u[n m]-u
[n m-1])/k" "6#*&,&&%\"uG6#*&%\"nG\"\"\"%\"mGF*F*&F&6#,&*&F)F*F+F*F*F*
!\"\"F0F*%\"kGF0" }{TEXT -1 4 "  = " }{XPPEDIT 18 0 "alpha^2" "6#*$%&a
lphaG\"\"#" }{TEXT -1 1 " " }{XPPEDIT 18 0 "(u[n+1 m]-2*u[n m]+u[n-1 m
])/h^2" "6#*&,(&%\"uG6#,&%\"nG\"\"\"*&F*F*%\"mGF*F*F**&\"\"#F*&F&6#*&F
)F*F,F*F*!\"\"&F&6#,&F)F**&F*F*F,F*F2F*F**$%\"hGF.F2" }{TEXT -1 3 "   \+
" }}{PARA 4 "" 0 "" {TEXT -1 68 "Se escribe el segundo para  m+1  en l
ugar de  m , y se toma la media" }}{PARA 4 "" 0 "" {TEXT -1 70 "aritm
\351tica de ambos, pero con coeficientes  1/4  y  3/4 , obteni\351ndos
e" }}{PARA 4 "" 0 "" {TEXT -1 31 "as\355 un m\351todo mezcla de ambos \+
." }}{PARA 4 "" 0 "" {TEXT -1 64 "Construir matricialmente dicho m\351
todo y comprobar que es estable" }}{PARA 4 "" 0 "" {TEXT -1 65 "con in
dependencia de las relaciones entre  h  y  k , incrementos " }}{PARA 
4 "" 0 "" {TEXT -1 16 "en  x  y en  t ." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 
"interface(labeling=false):" }}}{EXCHG {PARA 4 "" 0 "" {TEXT -1 36 "Es
tabilidad por el m\351todo de Fourier" }{MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "u:=(n,m)->exp(I*n*b*h)*exp(m*d*k);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"uGf*6$%\"nG%\"mG6\"6$%)operato
rG%&arrowGF)*&-%$expG6#**9$\"\"\"%\"bGF3%\"hGF3^#F3F3F3-F/6#*(9%F3%\"d
GF3%\"kGF3F3F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 103 "igua
ldad:=u(n,m+1)-u(n,m)-(lambda/4)*(u(n+1,m)-2*u(n,m)+u(n-1,m)+3*u(n+1,m
+1)-6*u(n,m+1)+3*u(n-1,m+1));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%)ig
ualdadG,(*&-%$expG6#**%\"nG\"\"\"%\"bGF,%\"hGF,^#F,F,F,-F(6#*(,&%\"mGF
,F,F,F,%\"dGF,%\"kGF,F,F,*&F'F,-F(6#*(F4F,F5F,F6F,F,!\"\"*&#F,\"\"%F,*
&%'lambdaGF,,.*&-F(6#**,&F+F,F,F,F,F-F,F.F,F/F,F,F8F,F,*(\"\"#F,F'F,F8
F,F;*&-F(6#**,&F+F,F,F;F,F-F,F.F,F/F,F,F8F,F,*(\"\"$F,FCF,F0F,F,*(\"\"
'F,F'F,F0F,F;*(FOF,FJF,F0F,F,F,F,F;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 55 "igualdad:=simplify(igualdad/(exp(I*n*b*h)*exp(m*d*k))
);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)igualdadG,.*(-%$cosG6#*&%\"bG
\"\"\"%\"hGF,F,%'lambdaGF,-%$expG6#*&%\"dGF,%\"kGF,F,#!\"$\"\"#*&#F,F7
F,*&F'F,F.F,F,!\"\"F/F,F,F;*(#\"\"$F7F,F.F,F/F,F,*&#F,F7F,F.F,F," }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "igualdad:=subs(cos(b*h)=1-2*
(sin(b*h/2))^2,igualdad);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)iguald
adG,.*(,&\"\"\"F(*&\"\"#F()-%$sinG6#,$*&%\"bGF(%\"hGF(#F(F*F*F(!\"\"F(
%'lambdaGF(-%$expG6#*&%\"dGF(%\"kGF(F(#!\"$F**&#F(F*F(*&F'F(F5F(F(F4F6
F(F(F4*(#\"\"$F*F(F5F(F6F(F(*&F3F(F5F(F(" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 29 "igualdad:=simplify(igualdad);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%)igualdadG,.*&%'lambdaG\"\"\"-%$expG6#*&%\"dGF(%\"kGF
(F(\"\"$**F/F(F'F(F)F()-%$cosG6#,$*&%\"bGF(%\"hGF(#F(\"\"#F:F(!\"\"F'F
(*&F'F(F1F(F;F)F(F(F;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "ig
ualdad:=subs(exp(d*k)=z,igualdad);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
>%)igualdadG,.*&%'lambdaG\"\"\"%\"zGF(\"\"$**F*F(F'F(F)F()-%$cosG6#,$*
&%\"bGF(%\"hGF(#F(\"\"#F5F(!\"\"F'F(*&F'F(F,F(F6F)F(F(F6" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "ealadk:=solve(igualdad,z);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'ealadkG,$*&,(\"\"\"F(%'lambdaG!\"\"
*&F)F()-%$cosG6#,$*&%\"bGF(%\"hGF(#F(\"\"#F5F(F(F(,(F)!\"$*(\"\"$F(F)F
(F,F(F(F(F*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "ealadk1:
=(1-lambda*sin(1/2*b*h)^2)/(1+3*lambda*sin(1/2*b*h)^2);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>%(ealadk1G*&,&\"\"\"F'*&%'lambdaGF')-%$sinG6#,$
*&%\"bGF'%\"hGF'#F'\"\"#F3F'!\"\"F',&F'F'*(\"\"$F'F)F'F*F'F'F4" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "simplify(ealadk1-ealadk);" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}}{MARK "0 3 0" 15 }
{VIEWOPTS 1 1 0 3 4 1802 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }