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February 18th, 2017, 09:53 AM   #1
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Galerkin Method Sine Series Expansion

I'm currently working on a 2-D Finite Difference code in MATLAB and am trying to check the approximations with the exact solution. Unfortunately I don't know how to employ the Galerkin Method to solve the given equation for exact results. Problem statement is attached. Any help is appreciated on solving this 2-D problem.
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February 18th, 2017, 12:08 PM   #2
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In case the picture is unclear,

-(∂²u/∂x² + ∂²u/∂y²) + uk² = xk²

u = u(x,y) u is a function of x and y

Boundary conditions are zero of the square domain (0,1)×(0,1)

Determine an exact solution in the form of a sine series expansion by employing the Galerkin Method.

Last edited by skipjack; February 18th, 2017 at 08:16 PM.
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