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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 243 "In this simulation, we so
lve the chemical mixing problem, with the chemical entering the reacto
r from the left end, and the mixture exitinf from the right end. The e
quation of the equilibrium solution is u''(x)=0, u'(0)=-2, and u'(1)+u
(1)=0.  " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "with(PDEtools);" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 39 "First we solve the equilibrium equ
ation" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "eq1:=diff(u(x),x,x)=0; gen
eral_solution:=dsolve(\{eq1\},u(x));" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 47 "dsolve(\{eq1,D(u)(0)=-2,D(u)(1)+u(1)=0\},\{u(x)\});" 
}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 169 "Next we solve the diffusion eq
uation with the initial condition u=0 by numerical method. When the ti
me is large, the solution will approach the equilibirum solved above.
" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "diffusion:=diff(u(t,x),t)=2*dif
f(u(t,x),x,x);" }}}{EXCHG }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "I
BC:=\{u(0,x)=0, D[2](u)(t,0)=-2, D[2](u)(t,1)+u(t,1)=0\};" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "pds:=pdsolve(diffusion, IBC, numeri
c, spacestep=1/40);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "pds:
-animate(t=2,frames=100);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
68 "IBC1:=\{u(0,x)=10*sin(Pi*x), 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(diffu
sion, IBC1, numeric, spacestep=1/40);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 32 "pds1:-animate(t=0.2,frames=100);" }}}{EXCHG {PARA 0 "
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