poisson equation
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 
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.

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