
bad PDE solution...
Posted:
Jan 14, 2013 12:01 AM


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.

