Comparison of the solutions obtained by Adomian decomposition and wavelet-Galerkin methods of boundary-value problems

Abstract

In this paper, we will compare the performance of Adomian decomposition method and the wavelet-Galerkin method applied to the solution of boundary-value problems involving non-homogeneous heat and wave equations. It is shown that the Adomian decomposition method in many instances gives better results. In the wavelet-Galerkin solutions, Daubechies six wavelets are used because they give better results than those of lower degree wavelets. The results are then compared with those obtained using the Adomian decomposition method. Although the Adomian decomposition solution required slightly more computational effort than the wavelet-Galerkin solution, it resulted in more accurate results than the wavelet-Galerkin method.