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"with(plots):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 210 91 "L is the length
 of spatial interval; k is the time step; h is the grid size(spatial s
tep); " }}{PARA 0 "" 0 "" {TEXT 210 65 "T is the maximum time to be co
mputed; d is the diffusion constant" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
38 "L:=1; k:=0.005; h:=0.10; T:=2; d:=0.1;" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT 210 60 "r and c are the constants appearing in the iteration for
mula" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "r:= d*k/h^2; c:=1-2*r;" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT 210 10 "parameter " }{XPPEDIT 18 0 "Types
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 "" 0 "" {TEXT 210 17 "Nonlinearity f(u)" }}{PARA 0 "> " 0 "" {MPLTEXT
 1 0 14 "f:=u->u*(1-u);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 210 17 "Initi
al Condition" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "u0:=y->evalf(0.2*si
n(Pi*y)); plot(u0(y), y=0..L);" }{TEXT 210 0 "" }}}{EXCHG {PARA 0 "" 0
 "" {TEXT 210 29 "Dirichlet boundary conditions" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 25 "left:=y->0; right:=y->0; " }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT 210 26 "Generate the spatial grids" }}{PARA 0 "> " 0 "" {MPLTEXT
 1 0 44 "n:=floor(L/h)+1; x:=[seq(0+(i-1)*h,i=1..n)];" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT 210 24 "Generate the time grids " }}{PARA 0 "> "
 0 "" {MPLTEXT 1 0 44 "m:=floor(T/k)+1; t:=[seq(0+(j-1)*k,j=1..m)];" }
}}{EXCHG {PARA 0 "" 0 "" {TEXT 210 38 "Initialize the solution matrix \+
by zero" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "u:=matrix(n,m,[seq([seq(
0.0,j=1..m)],i=1..n)]):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 210 23 "Input
 the initial value" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "for i from 1 \+
to n do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "     u[i,1]:=u0(x[i]);" 
}}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "end:" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT 210 29 "Input the boundary conditions" }{MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "for j from 1 to m-1 do" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "     u[1,j+1]:=left(t[j]); u[n,j+1]
:=right(t[j]);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "end:" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT 210 43 "Compute the matrix by the iteration form
ula" }{MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "for j fro
m 1 to m-1 do  " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "   for i from 2 \+
to n-1 do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "      u[i, j+1]:=r*u[i
-1,j]+c*u[i,j]+r*u[i+1,j]+lambda*k*f(u[i,j]); " }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 10 "   end do;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "end d
o:" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT 209 9 "Animation" }}{EXCHG 
{PARA 0 "" 0 "" {TEXT 210 70 "Each of the following is a static plot o
f the solution at a given time" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 20 "for j from 1 to m do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "  U
[j]:=plot([seq([x[i],u[i,j]],i=1..n)]);" }}{PARA 0 "> " 0 "" {MPLTEXT 
1 0 7 "end do:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 210 58 "display the se
quence of the static plots into an animation" }{MPLTEXT 1 0 0 "" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "display([seq(U[j],j=1..m)], inseque
nce=true);" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "" "%#%?G" }}}
{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "" "%#%?G" }}}{EXCHG {PARA 209 
"" 0 "" {TEXT 207 46 "**** THIS IS A PLOT THAT CAN BE ANIMATED *****" 
}}}}}
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 33 1 1 }