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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 113 "d1:= (u(n+1,i) - u(n,i))/dt + a*(u
(n,i+1) - u(n,i-1))/(2*dx) - a^2*dt/(2*dx^2)*(u(n,i+1) - 2*u(n,i) + u(
n,i-1));\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#d1G,(*&,&-%\"uG6$,&%
\"nG\"\"\"F-F-%\"iGF--F)6$F,F.!\"\"F-%#dtGF1F-*&#F-\"\"#F-*(%\"aGF-,&-
F)6$F,,&F.F-F-F-F--F)6$F,,&F.F-F-F1F1F-%#dxGF1F-F-*&#F-F5F-**F7F5F2F-F
?!\"#,(F9F-*&F5F-F/F-F1F<F-F-F-F1" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 10 "Order:=4;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&Ord
erG\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 122 "u := (argn,arg
i) -> \n    convert(mtaylor(\n      uu(t + dt*(argn - n),x+dx*(argi - \+
i)),\n      [dt=0,dx=0],Order),polynom);\n" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"uGf*6$%%argnG%%argiG6\"6$%)operatorG%&arrowGF)-%(co
nvertG6$-%(mtaylorG6%-%#uuG6$,&%\"tG\"\"\"*&%#dtGF8,&9$F8%\"nG!\"\"F8F
8,&%\"xGF8*&%#dxGF8,&9%F8%\"iGF>F8F87$/F:\"\"!/FBFH%&OrderG%(polynomGF
)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "u(n+1,i+1);\n" }}
{PARA 12 "" 1 "" {XPPMATH 20 "6#,6-%#uuG6$%\"tG%\"xG\"\"\"*&--&%\"DG6#
F)6#F%F&F)%#dtGF)F)*&--&F.6#\"\"#F0F&F)%#dxGF)F)*&#F)F7F)*&--&F.6$F)F)
F0F&F))F1F7F)F)F)*(--&F.6$F)F7F0F&F)F1F)F8F)F)*&F:F)*&--&F.6$F7F7F0F&F
))F8F7F)F)F)*&#F)\"\"'F)*&--&F.6%F)F)F)F0F&F))F1\"\"$F)F)F)*&F:F)*(--&
F.6%F)F)F7F0F&F)F@F)F8F)F)F)*&F:F)*(--&F.6%F)F7F7F0F&F)F1F)FLF)F)F)*&F
NF)*&--&F.6%F7F7F7F0F&F))F8FVF)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 40 "eq1 := simplify(subs(dt=lambda*dx,d1));\n" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%$eq1G,.*&#\"\"\"\"\"'F(*(--&%\"DG6%F(F(F(6
#%#uuG6$%\"tG%\"xGF()%'lambdaG\"\"#F()%#dxGF7F(F(F(*&#F(F7F(*(--&F.6$F
(F(F0F2F(F6F(F9F(F(F(--&F.6#F(F0F2F(*&F'F(*(--&F.6%F7F7F7F0F2F(%\"aGF(
F8F(F(F(*&--&F.6#F7F0F2F(FKF(F(*&#F(F7F(**)FKF7F(F6F(F9F(--&F.6$F7F7F0
F2F(F(!\"\"" }}}{EXCHG {PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 33 "sol := solve(eq1,D[1](uu)(t,x));\n" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$solG,,*&#\"\"\"\"\"'F(*(--&%\"DG6%F
(F(F(6#%#uuG6$%\"tG%\"xGF()%'lambdaG\"\"#F()%#dxGF7F(F(!\"\"*&#F(F7F(*
(--&F.6$F(F(F0F2F(F6F(F9F(F(F:*&#F(F)F(*(--&F.6%F7F7F7F0F2F(%\"aGF(F8F
(F(F:*&--&F.6#F7F0F2F(FIF(F:*&#F(F7F(**)FIF7F(F6F(F9F(--&F.6$F7F7F0F2F
(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "eq2 := algsubs(dx^
3=0,simplify(subs(D[1$2](uu)(t,x) = diff(sol,t$1),eq1)));\n" }}{PARA 
12 "" 1 "" {XPPMATH 20 "6#>%$eq2G,**&,&*&#\"\"\"\"\"#F**(%'lambdaGF*--
&%\"DG6$F*F+6#%#uuG6$%\"tG%\"xGF*%\"aGF*F*!\"\"*&#F*F+F**()F8F+F*F-F*-
-&F16$F+F+F3F5F*F*F9F*%#dxGF*F**&,(*&#F*\"#7F**&--&F16%F*F*F*F3F5F*)F-
F+F*F*F9*&#F*\"\"%F**(FMF*F=F*--&F16%F*F+F+F3F5F*F*F**&#F*\"\"'F**&--&
F16%F+F+F+F3F5F*F8F*F*F*F*)FBF+F*F**&--&F16#F+F3F5F*F8F*F*--&F16#F*F3F
5F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 85 "eq3 := collect(algsu
bs(dx^3=0,simplify(subs(D[1,2](uu)(t,x) = diff(sol,x),eq2))),D);\n" }}
{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$eq3G,.--&%\"DG6#\"\"\"6#%#uuG6$%\"t
G%\"xGF+*&--&F)6#\"\"#F,F.F+%\"aGF+F+*&#F+\"#7F+*(--&F)6%F+F+F+F,F.F+)
%'lambdaGF6F+)%#dxGF6F+F+!\"\"*&#F+\"\"%F+**F7F+F@F+--&F)6%F+F+F6F,F.F
+FBF+F+F+*&FFF+**F@F+FBF+)F7F6F+--&F)6%F+F6F6F,F.F+F+F+*(,&*&#F+FGF+*&
)F7\"\"$F+F@F+F+FD*&#F+\"\"'F+F7F+F+F+FBF+--&F)6%F6F6F6F,F.F+F+" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 87 "eq4 := collect(algsubs(dx^3=
0,simplify(subs(D[1$3](uu)(t,x) = diff(sol,t$2),eq3))),D);\n" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%$eq4G,,--&%\"DG6#\"\"\"6#%#uuG6$%\"tG%\"xG
F+*&--&F)6#\"\"#F,F.F+%\"aGF+F+*&#F+\"\"$F+**F7F+)%'lambdaGF6F+--&F)6%
F+F+F6F,F.F+)%#dxGF6F+F+F+*&#F+\"\"%F+**F<F+FBF+)F7F6F+--&F)6%F+F6F6F,
F.F+F+F+*(,&*&#F+FFF+*&)F7F:F+F<F+F+!\"\"*&#F+\"\"'F+F7F+F+F+FBF+--&F)
6%F6F6F6F,F.F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 89 "eq5 := \+
collect(algsubs(dx^3=0,simplify(subs(D[1$2,2](uu)(t,x) = diff(sol,t,x)
,eq4))),D);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eq5G,*--&%\"DG6#\"
\"\"6#%#uuG6$%\"tG%\"xGF+*&--&F)6#\"\"#F,F.F+%\"aGF+F+*&#F+\"#7F+**)%'
lambdaGF6F+)%#dxGF6F+)F7F6F+--&F)6%F+F6F6F,F.F+F+!\"\"*(,&*&#F+\"\"%F+
*&)F7\"\"$F+F<F+F+FE*&#F+\"\"'F+F7F+F+F+F>F+--&F)6%F6F6F6F,F.F+F+" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 96 "eq6 := collect(algsubs(dx^3=
0,simplify(subs(D[1,2$2](uu)(t,x) = diff(sol,x$2),eq5))),D,factor);\n
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eq6G,(--&%\"DG6#\"\"\"6#%#uuG6$
%\"tG%\"xGF+*&--&F)6#\"\"#F,F.F+%\"aGF+F+*&#F+\"\"'F+*,F7F+)%#dxGF6F+,
&*&F7F+%'lambdaGF+F+F+!\"\"F+,&*&F7F+F@F+F+F+F+F+--&F)6%F6F6F6F,F.F+F+
FA" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "13 0 0" 0 }{VIEWOPTS 1 1 0 1 1 
1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }