TREATMENT OF BOUNDARY-CONDITIONS IN ONE-DIMENSIONAL WAVELET-GALERKIN METHOD

One of the main problems of the Wavelet-Galerkin Method is the treatme nt of boundary conditions. To deal with this difficulty, the boundarie s of wavelet series expansion are assumed to be the analytic boundarie s of the problem. The boundary condition equations are replaced by end equations in the Galerkin system. The manipulation discussed here ena bles us to use classical wavelets and to tackle the problem more simpl y. However, we find that the end equations are a necessary part of the Galerkin equation system within the boundaries. To maintain the integ rity of the system, the boundaries of wavelet series expansion are shi fted until the end equations do not depend on any expansion coefficien ts c(k) of phi(2(j)x-k) that affect the solution within the real bound aries. Therefore replacing the end equations gives a good result in co mparison to the exact solution.