# Spectral Method Boundary condition

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 February 25, 2004, 05:13 Spectral Method Boundary condition #1 Deepak Guest   Posts: n/a 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,

 February 25, 2004, 09:48 Re: Spectral Method Boundary condition #2 Tom Guest   Posts: n/a 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.