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