ADE details

A Partial Differential Equation Approach

ADE details

Postby avk » Thu Feb 10, 2011 4:12 pm


I am trying to get an understanding how ADE is formed. Looking at the paper on ADE I have a couple of questions:

1. the second derivatives are presented as a linear combination of 4 points, I can't see where the approximation is done, at which point? I was trying to do Taylor around but could not hit the same approximation.

2. the method is called "explicit". What I am confused is looking at the representation there are as many unknown points at n+1 level in time direction as the dimensionality of the equation, so it is not quite explicit, is there a matrix equation to be solved at every level or not?

I'd appreciate any insights. Thanks!
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Postby Cuchulainn » Mon Feb 14, 2011 9:34 am

Here is the 1st paper in 1d, see equations (33), (34) , everything on the right is known because we have Dirichlet BC ... id=1552926

The 3d case is just a cube.


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