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 November 13th, 2016, 04:40 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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