Legendre wavelet Galerkin method for semi-discretizing one dimensional diffusion equations

Abstract

In this paper, we develop a Legendre wavelet Galerkin method for semi-discretizing one dimensional diffusion equations. Since the Legendre wavelet functions do not satisfy the boundary conditions of the problem, the Galerkin bases are obtained by integrating Legendre wavelet functions. The orthonormality and other properties of Legendre wavelets are used to transform initial-boundary value problems governed by diffusion equations into systems of ordinary differential equations