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{SECT 0 {PARA 3 "" 0 "" {TEXT 209 16 "Matrix Algorithm" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "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 step); " }}{PARA 0 "" 0 "" {TEXT 210 
65 "T is the maximum time to be computed; d is the diffusion constant"
 }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "L:=1; k:=0.05; h:=0.10; T:=2; d:
=0.1;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 210 60 "r and c are the constan
ts appearing in the iteration formula" }}{PARA 0 "> " 0 "" {MPLTEXT 1 
0 22 "r:= d*k/h^2; c:=1-2*r;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 210 17 "
Initial Condition" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "u0:=y->evalf(s
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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
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{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 \+
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0.0,j=1..m)],i=1..n)]):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 210 23 "Input
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{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]
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{PARA 0 "" 0 "" {TEXT 210 43 "Compute the matrix by the iteration form
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m 1 to m-1 do  " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "   for i from 2 \+
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{PARA 3 "" 0 "" {TEXT 209 9 "Animation" }}{EXCHG {PARA 0 "" 0 "" {TEXT
 210 70 "Each of the following is a static plot of the solution at a g
iven time" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "for j from 1 t
o 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 sequence of the stati
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{MPLTEXT 1 0 45 "display([seq(U[j],j=1..m)], insequence=true);" }}}
{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "" "%#%?G" }}}{EXCHG {PARA 210 
"" 0 "" {TEXT 207 46 "**** THIS IS A PLOT THAT CAN BE ANIMATED *****" 
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