[jangolobow]

Hallo,
does there exist analytical solution or approximation to poisson equation pde in 2 dimensions
D[u,x,x]+D[u,y,y]=ax^4+b*x^3+c*x^2+d*x+e
ax^4+b*x^3+c*x^2+d*x+e is polinom
where BC are
u[x,1]=2
u[x,0]=0
u[2,y]=0
u[0,y]=0
where a,b,c,d,e are constants (real number)
Or if somebody knows where to look for this solution!
Thanks,
JG

[agd]

You can solve this equation (at least formally) in an analytical sense using the projection method, which is a generalization of the eigenfunction expansion method. You should be able to find this approach in any reasonably good book on PDEs.