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Re: question about NDSolve for Diffusion equation

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  • Subject: [mg102840] Re: [mg102823] question about NDSolve for Diffusion equation
  • From: "Ingolf Dahl" <ingolf.dahl at>
  • Date: Sat, 29 Aug 2009 06:31:07 -0400 (EDT)
  • References: <>

First things first:
Is this really the diffusion equation? With the second derivative in t it
looks more like the wave equation.
But then, look in the MathGroup archive, less than one year back, for the
threads "Diffusion Model using NDSolve - Advice needed", "PDE heat equation
(inconsisten problem)" and "Partial differential equation with evolving
boundary conditions". I think you have stumbled on the same problems as
discussed there, not a mathematical necessity but a bug-like feature of the
solution method used by Mathematica. I hope you will find something
interesting or useful for your problem there. I think your letter is a FAQ,
and I think you should avoid the sharp change of C[0,t] near t=0. You might
try with a ramp in a short time interval. There are also other methods

Best regards

Ingolf Dahl

> -----Original Message-----
> From: Nam Viet Nguyen [mailto:teivn109 at] 
> Sent: den 28 augusti 2009 06:46
> To: mathgroup at
> Subject: [mg102823] question about NDSolve for Diffusion equation
> Hello,
> I am trying to use the NDSolve of Mathematica to solve the 
> diffusion equation which has diffusivity dependence to 
> concentration. My work is dealing with phosphorous diffusion 
> into silicon.
> The equation is
> d''C/dt^2 = d( C^2 *dC/dx)/dx
> where C= C(x,t).
> In my problem, the initial conditions should be : C(x,0)=0, 
> C(0,0) = 0, C(0,t) = Cs if t > 0. 
> If I used the NDSolve, there is a error message, the Initial 
> conditions are not consistent.
> I dont known how to go further as I have checked again and 
> again the initial conditions are fine. 
> Your helps anf advice are gratefully acknowledged,
> Nam Nguyen.
> Stuttgart, Germany

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