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MathGroup Archive 2005

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Re: Getting good results with NDSolve?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg62938] Re: Getting good results with NDSolve?
  • From: dh <dh at metrohm.ch>
  • Date: Fri, 9 Dec 2005 05:10:17 -0500 (EST)
  • References: <dn8g3t$bqd$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hi Christopher,
something is fishy with your expression:

dg/dt = Norm(Grad g) * Laplacian(Grad g / Norm (Grad g))

On the left side you have a scalar.
On the right side you have Laplacian(Grad g ...) what is a vector.

Maybe you mean Div( Grad g / Norm (Grad g))?????

Daniel

pantagruel123 at aol.com wrote:
>  
> Hi, I'm experimenting with NDSolve, not being an expert with differential equations.  I'm getting some results, but it seems like I'm getting too much precision where I don't need it, and not enough where I do.  I'm wondering if playing with the options would be something worth trying.  Also it takes a really long time to compute what I've been told should take seconds with a C++ routine. 
>  
> If I want to solve a PDE of three variables (t,x,y) on the region {0,1}^3, how can I tell NDSolve to have, say a resolution of N x N points for (x,y) and a resolution of M for t?  I find that if I just reduce the max points for t, then NDSolve quits before gets to the end of the interval.  Maybe there is a way to tell NDSolve to trash some intermediate results and just keep every Mth point?
>  
> The equation i'm using is  dg/dt = Norm(Grad g) * Laplacian(Grad g / Norm (Grad g))
> where we're looking for g(t,x,y), and the right-hand derivatives are taken only with respect to x and y.  My initial value g(0,x,y) had been generated from a ListInterpolation--I'm guessing this is the best way to use a bitmap as the inital value.  
>  
> Regards,
>  
> Christopher Arthur
> 
> 


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