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November 13th, 2016, 05:40 AM  #1 
Newbie Joined: Nov 2016 From: Italy Posts: 1 Thanks: 0  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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elliptic, equation, pde, solve 
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