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February 18th, 2017, 02:43 PM   #1
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2-D Finite Difference 4th Order Equilibrium Approximation Derivation

I'm having issues deriving 4th order equations for my finite difference method.
I was able to do the second order but am confused on the 2-D 4th order derivation and was wondering if anyone could show me how to derive it in 2-D.

Attached is an example of how I was able to do 2nd and 4th order in 1-D. The boxed answered in the doc is what I'm trying to derive for the 2-d case.

The new equation i'd like to apply this to is u''+uk^2=xk^2 with 4th order approximation.

where u=u(x,y) and boundary conditions are zero for the Square Domain (0,1)X(0,1).
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