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Getting good results with NDSolve?

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.  
Christopher Arthur

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