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{SECT 0 {PARA 18 "" 0 "" {TEXT -1 40 "Finite Difference - Convection D
iffusion" }}{PARA 19 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 
122 "This worksheet illustrates the finite difference method for a sim
ple one-dimensional steady convection diffusion equation." }}{PARA 0 "
" 0 "" {TEXT -1 33 "Restart Maple and load libraries." }}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 32 "with(LinearAlgebra):with(plots):" }}{PARA 7 "" 1 "" 
{TEXT -1 50 "Warning, the name changecoords has been redefined\n" }}}
{PARA 0 "" 0 "" {TEXT -1 24 "We consider the equation" }}{PARA 256 "" 
0 "" {XPPEDIT 18 0 "-diff(u,x,x)+k*diff(u,x) = 0;" "6#/,&-%%diffG6%%\"
uG%\"xGF)!\"\"*&%\"kG\"\"\"-%%diffG6$%\"uG%\"xGF-F-\"\"!" }{TEXT -1 6 
"      " }{XPPEDIT 18 0 "u(0) = 0;" "6#/-%\"uG6#\"\"!F'" }{TEXT -1 5 "
     " }{XPPEDIT 18 0 "u(1) = 1;" "6#/-%\"uG6#\"\"\"F'" }{TEXT -1 0 "
" }}{PARA 0 "" 0 "" {TEXT -1 21 "define the parameter " }{XPPEDIT 18 
0 "k;" "6#%\"kG" }{TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 6 "k:=50;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"kG\"#]" }}}{PARA 0 
"" 0 "" {TEXT -1 26 "the number of grid points " }{XPPEDIT 18 0 "n;" "
6#%\"nG" }{TEXT -1 22 " and the mesh spacing " }{XPPEDIT 18 0 "h;" "6#
%\"hG" }{TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "n:=11
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" 0 "" {MPLTEXT 1 0 11 "h:=1/(n-1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#>%\"hG#\"\"\"\"#5" }}}{PARA 0 "" 0 "" {TEXT -1 66 "After discretizati
on we get a system of linear algebraic equations" }}{PARA 256 "" 0 "" 
{XPPEDIT 18 0 "Au = b;" "6#/%#AuG%\"bG" }{TEXT -1 0 "" }}{PARA 0 "" 0 
"" {TEXT -1 29 "define the matrix and vectors" }}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 15 "A:=Matrix(n,n);" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#>%\"AG-%'RTABLEG6+\")#pm#=%)anythingG%'MatrixG%,rectangularG%.Fortr
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1 0 13 "u:=Vector(n);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"uG-%'RTAB
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\";F1\"#6" }}}{PARA 0 "" 0 "" {TEXT -1 4 "set " }{XPPEDIT 18 0 "f[1];
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%\"fG6#%\"nG" }{TEXT -1 36 "  to account for boundary conditions" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "f[1]:=0;" }}{PARA 11 "" 1 "" 
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{MPLTEXT 1 0 8 "f[n]:=1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"fG6#
\"#6\"\"\"" }}}{PARA 0 "" 0 "" {TEXT -1 35 "Compute the elements of th
e matrix " }{XPPEDIT 18 0 "A;" "6#%\"AG" }{TEXT -1 34 " using centered
 finite differences" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "for i
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{MPLTEXT 1 0 7 "end do:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "
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0 "" 0 "" {TEXT -1 61 "set first and last equation to account for boun
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" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"AG6$\"\"\"F'F'" }}}{EXCHG 
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{XPPMATH 20 "6#>&%\"AG6$\"#6F'\"\"\"" }}}{PARA 0 "" 0 "" {TEXT -1 19 "
solve linear system" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "u:=Li
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I5RTABLE_SAVE/18233348X*%)anythingG6"6"[gl!#%!!!",",""!F'F'F'F'F'F'F'F'F'F'6"
}
{RTABLE 
M7R0
I5RTABLE_SAVE/16145620X*%)anythingG6"6"[gl!#%!!!",",""!F'F'F'F'F'F'F'F'F'"""6"
}
{RTABLE 
M7R0
I5RTABLE_SAVE/18233428X*%)anythingG6"6"[gl!#%!!!",",""!#!&$o>")?;CG#"%hl"(0/1(#
!&>4)F*#"&#GUF-#!$V#"&kl"#"'jnBF-#!(r%HAF*#"(/cH"F-#!)()>67F*"""6"
}
{RTABLE 
M7R0
I5RTABLE_SAVE/18233548X*%)anythingG6"6"[gl!#%!!!",",""!#"$7&")X[\c#"$c#"(0sF'#"
%w&)F*#"%#R$F-#"#K"&Ro"#"&3=%F-#"(kuJ"F*#"'/C^F-#")Q79;F*"""6"
}