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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "with(PDEtools): diff
usion:=diff(u(t,x),t)=2*diff(u(t,x),x,x);" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 52 "pdsolve(diffusion, u(t,x), HINT=X(x)*T(t), 'build')
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t=0.2,frames=100);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 14 "Robin Bound
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D[2](u)(t,0)=-2, D[2](u)(t,1)+u(t,1)=0\};" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 56 "pds1:=pdsolve(diffusion, IBC1, numeric, spacestep=1
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2,frames=500);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "Periodic Bounda
ry" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "IBC2:=\{u(0,x)=exp(-0.2*x), D
[2](u)(t,0)=D[2](u)(t,1), u(t,0)=u(t,1)\};" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 57 "pds2:=pdsolve(diffusion, IBC2, numeric, spacestep=1
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.2,frames=500);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 31 "Smoothering ef
fect of diffusion" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 169 "p1:=pds2:-plo
t(t=0,numpoints=50, color=red):\np2:=pds2:-plot(t=0.01,numpoints=50,co
lor=blue):\np3:=pds2:-plot(t=0.02,numpoints=50,color=green):\nplots[di
splay](\{p1,p2,p3\});" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "IB
C3:=\{u(0,x)=sin(20*x), D[2](u)(t,0)=D[2](u)(t,1), u(t,0)=u(t,1)\};" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "pds3:=pdsolve(diffusion, I
BC3, numeric, spacestep=1/160);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 169 "p4:=pds3:-plot(t=0,numpoints=50, color=red):\np5:=pds3:-plot(
t=0.01,numpoints=50,color=blue):\np6:=pds3:-plot(t=0.02,numpoints=50,c
olor=green):\nplots[display](\{p4,p5,p6\});" }}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 36 "Anti-smoothing of backward diffusion" }}{PARA 0 "> " 0 
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=pds3:-plot(t=-0.01,numpoints=50,color=blue):\np6:=pds3:-plot(t=-0.02,
numpoints=50,color=green):\nplots[display](\{p4,p5,p6\});" }}}{EXCHG 
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