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February 18th, 2017, 01:43 PM  #1 
Newbie Joined: Feb 2017 From: College Station Posts: 7 Thanks: 0  2D 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 2D 4th order derivation and was wondering if anyone could show me how to derive it in 2D. Attached is an example of how I was able to do 2nd and 4th order in 1D. The boxed answered in the doc is what I'm trying to derive for the 2d 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). 

Tags 
4th, approximation, derivation, difference, equilibrium, finite, order 
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