Solve PDE - elliptic equation
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Hi, I have to solve this PDE:
Uxx+Uxy+Uyy+sin(u)=12∗(x2+y2)+sin(x2+y2)Uxx+Uxy+Uyy+sin(u)=12∗(x2+y2)+sin(x2+y2)
The domain is
U(0,y)=y4;U(1,y)=1+y4;U(x,0)=x4;U(x,1)=1+x4;U(0,y)=y4;U(1,y)=1+y4;U(x,0)=x4;U(x,1)=1+x4;
First of all I think that I change the equations in canonical form, I do this with:
(eta=((3)(1/2)x/2),(ξ=y−(1/2)x):(eta=((3)(1/2)x/2),(ξ=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
1 comentario
Torsten
el 15 de Nov. de 2016
If the domain is rectangular for the original equation, it's better to leave everything as it is. Schemes to discretize Uxy are standard.
Best wishes
Torsten.
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