Re: question about NDSolve for Diffusion equation

*To*: mathgroup at smc.vnet.net*Subject*: [mg102840] Re: [mg102823] question about NDSolve for Diffusion equation*From*: "Ingolf Dahl" <ingolf.dahl at telia.com>*Date*: Sat, 29 Aug 2009 06:31:07 -0400 (EDT)*References*: <200908280446.AAA28981@smc.vnet.net>

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 available. Best regards Ingolf Dahl > -----Original Message----- > From: Nam Viet Nguyen [mailto:teivn109 at yahoo.com] > Sent: den 28 augusti 2009 06:46 > To: mathgroup at smc.vnet.net > 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 > >

**References**:**question about NDSolve for Diffusion equation***From:*Nam Viet Nguyen <teivn109@yahoo.com>