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bad PDE solution...

  • To: mathgroup at smc.vnet.net
  • Subject: [mg129440] bad PDE solution...
  • From: Fred Bartoli <""@news.free.fr>
  • Date: Mon, 14 Jan 2013 00:03:10 -0500 (EST)
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  • Reply-to: myname_with_a_dot_inbetween at free.fr

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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