Hi all, I am working with spectral method to resolve 2D partial differential equation in 2D. I have two boundary condition for each of the 4 boundary. I dont know how to impose the boundary conditions as in spectral method(using collocation) number of equations are same as number of collocation points.... if i take just one of the boundary condition then i have equal number of equations ans unknowns and if i intend to incorporate both the boundary condition then i have more equations for the same number of unknowns. I tried using multiple collocation point on the boundary but .. then i have zero diagonal elements in the final matrix.. at three of the neighbouring node(of each corner). can someone help me here?? Thanx in advance,

Basically you need to remove the equations near the boundary and replace them by the boundary condtions; i.e you have something like (in 1D)

u = a_1.P_1 + a_2.P_2 + ... + a_N.P_N

where P_j(x) are your basis functions. If you now use N-k (where k is the number of boundary conditions that need to be applied - 4 in your case) collocation points then you can prescribe your boundary conditions in the remaining k equations.

( If P_N is a Tchybshev polynomial for example you would use the zeroes of the next polymial (P_N+1) as yor collocation points and throw away the zeroes nearest the wall )

Tom.