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bad PDE solution...
Posted:
Jan 14, 2013 12:01 AM
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Hello,
As a first simple test case of a more complicated pb I want to solve the
plane diffusion equation.
It seems NDSolve gives a bad answer to the simple step case but I can't
find what's happening...
(* Set up the equation: *)
eq1=D[h[t,x],x,x]- k1 D[h[t,x],t]==0
const=k1-> 10000
(*"solve" it...*)
sol = NDSolve[
{D[h[t, x], {x, 2}] - k1 D[h[t, x], t] == 0, h[0, x] == 0,
h[t, 1] == 0, h[t, 0] == 1 - Exp[-10^6*t]} /. const,
h, {t, 0, 10^-3}, {x, 0, 0.01}][[1]]
Plot3D[(h[t,x])/.mag/.solCart,{x,0,10^-4},{t,0,10^-4},AxesLabel->{"x","t","h"},PlotRange->All,PlotLabel->"Bogus
solution"]
Plot3D[Erfc[x/(2*Sqrt[t/k1])]/.const,{x,0,10^-4},{t,0,10^-4},AxesLabel->{"X","t","h"},PlotRange->All,PlotLabel->"The
right one"]
(* Test the Erfc[x/(2Sqrt[t/k1])] solution *)
Release[Hold[D[h[t,x],x,x]- k1*D[h[t,x],t]]/.
h[t,x]->Erfc[x/(2*Sqrt[t/k1])]]//Simplify
I hope I'm doing something wrong, but I can find what...
--
Thanks,
Fred.
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