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MathGroup Archive 2005

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Re: NDSolve

  • To: mathgroup at smc.vnet.net
  • Subject: [mg62660] Re: NDSolve
  • From: Paul Abbott <paul at physics.uwa.edu.au>
  • Date: Wed, 30 Nov 2005 00:08:12 -0500 (EST)
  • Organization: The University of Western Australia
  • References: <dlkc4b$ppg$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

In article <dlkc4b$ppg$1 at smc.vnet.net>,
 Uli Wuerfel <uli.wuerfel at fmf.uni-freiburg.de> wrote:

> I reduced it to a simple diffusion equation, but still it does not work.
> My Input is like:
> 
> dcb=0.001;
> rcb=1000;
> gen=5e20;
> ab=2000;
> d=0.001;
> 
> sol=nc/.First[NDSolve[
> {0==dcb*nc(2)[x]+gen*Exp[-ab*x]-rcb*(nc-nc0),
> nc[0]==nc0,nc(1)[d]==0},nc,{x,0,d}]]
> 
> wherein nc(i)[x] stands for the i-th spatial derivative of nc[x].
> 
> I don´t understand why Mathematica does not accept this.

First note that Mathematica can solve this problem exactly:

   DSolve[{0 == dcb nc''[x] + gen/E^(ab x) - rcb (nc[x] - nc0), 
    nc[0] == nc0, nc'[d] == 0}, nc, x]

There are three problems with your above code:

[1] gen=5e20 is not numerical. However, you will encounter a problem 
with stiffness if you try gen=5 10^20;

[2] You have not specified nc0.

[3] You have (nc-nc0) but nc is a function of x.

Fixing these problems, the following works fine:

 dcb = 0.001; 
 rcb = 1000; 
 gen = 5*10^10; 
 ab = 2000; 
 d = 0.001; 
 nc0 = 1; 

 sol = NDSolve[{0 == dcb nc''[x] + gen/E^(ab x) - rcb (nc[x] - nc0), 
    nc[0] == nc0, nc'[d] == 0}, nc, x]

 Plot[Evaluate[nc[x] /. sol], {x, 0, d}]

Cheers,
Paul

_______________________________________________________________________
Paul Abbott                                      Phone:  61 8 6488 2734
School of Physics, M013                            Fax: +61 8 6488 1014
The University of Western Australia         (CRICOS Provider No 00126G)    
AUSTRALIA                               http://physics.uwa.edu.au/~paul


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