Numerical Solution of Boundary Value Problem by Using Wavelet-Galerkin Method

In this paper we show that wavelets can be used as basis functions for Galerkin methods. For differential equations, finite element or finite difference methods lead to matrices that are already shown to be sparse, but they tend to be ill-conditioned, [4]. In this paper, we show that wavelet basis gives sparse matrix with low condition number for Galerkin methods. Numerical examples are presented to show the advantages of wavelet basis.