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Say we discretize some differential equation with the following iteration equation:

$\phi ^{n+1}(x,y)= \phi ^{n-1}(x,y) +f(x,y)\phi ^n$

(if you'd like some more specific example, let me know)

The problem is feeding this equation with two $\phi$ so we can start the iteration. We can assume that any continuous $\phi$ at a given instant is a part of a solution of the original equation, but two subsequent $\phi$ (even if very close) assumes a small evolution that might not be a solution of the original equation. Am I making any sense? To put the question in a more simple way: What is the usual approach of creating suitable initial conditions for 3 steps iteration equations?

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Depends on your problem. If you mention your actual problem, we might be a bit more helpful... –  J. M. Oct 31 '11 at 12:36
    
I want to see some real iteration equation or the original differential equation? or both? –  Diego Oct 31 '11 at 12:37
    
I don't know what you want, that's why I'm asking... –  J. M. Oct 31 '11 at 12:38

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