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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 88 "newtonian_slab_fouri
er.mws\n  Slab insulated on one face, newtonian heating at other face
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1107 "restart:\nNN:=10:\npi
:=evalf(Pi):\nguess:=pi/4;\nfor n from 1 to NN do\n  lambdas[n]:=fsolv
e(cos(lambda)=lambda*sin(lambda),lambda=guess);\n  guess:=lambdas[n]+p
i;\nod: unassign('n'):\ncheck_plot1:=plot([cos(lambda),lambda*sin(lamb
da)],lambda=0..(NN)*Pi,view=[0..(NN)*Pi+0.1,-1..1]):\ncheck_plot2:=plo
t([seq([lambdas[n],cos(lambdas[n])],n=1..NN)],style=point,color=black)
:\ncheck_plot3:=plot([seq([n*Pi,0],n=1..NN)],style=point,color=blue):
\nplots[display](check_plot3,check_plot2,check_plot1,title=\"Did we ge
t all the roots?\");\nC:=lambda->4*sin(lambda)/(2*lambda+sin(2*lambda)
);\nCs:=seq(C(lambdas[n]),n=1..NN);\ncheck_plot4:=plot([seq([n,abs(Cs[
n])],n=1..NN)],style=point):\ncheck_plot5:=plot(2/((n-1)^2*Pi^2),n=2..
NN):\nplots[display](check_plot4,check_plot5,title=\"Check the C estim
ate formula\",view=[0..NN,0..0.1]);\nDigits:=20;\nfor N from 1 to NN d
o\n  T:=1-add(Cs[n]*cos(lambdas[n]*(1-x))*exp(-lambdas[n]^2*t),n=1..N)
;\n  p[N]:=plot3d(T,x=0..1,t=0..2,title=convert(N,string)):\nod: unass
ign('N'):\n#plots[display](seq(p0[N],N=1..NN));\nplots[display](seq(p[
N],N=1..NN),insequence=true,axes=boxed, labels=\n['x','t','T']);\n" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&guessG$\"+N;)R&y!#5" }}{PARA 13 "" 
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