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November 13th, 2016, 05:40 AM   #1
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Solve PDE - elliptic equation

Hi,
I have to solve this PDE:

$ U_{xx} +U_ {xy}+U_{yy}+sin(u)=12*(x^2+y^2)+sin(x^2+y^2) $

The domain is

$ U(0, y)=y^4; U(1, y)=1+y^4; U(x, 0)=x^4; U(x, 1)=1+x^4; $

First of all I think that I change the equations in canonical form, I do this with:

$ { ( eta=((3)^(1/2)x/2 ),( ΞΎ=y-(1/2)x ):} $

This is quite easy. The problem is the domain: How can I transform in the new
coordinates?

I need a domain that is rectangular: I want to solve the equation with Jacobi iterative method.

Thanks
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