Numerical Solution of Singular Boundary Value Problems by Hermite Wavelet Based Galerkin Method

Abstract

Singular boundary value problems (SBVPs) occur frequently in various branches of applied mathematics, mechanics, and atomic theory and chemical sciences. In this paper, we proposed the numerical solution of SBVPs by Hermite wavelet based Galerkin method (HWMG). Here, Hermite wavelets are used as weight functions and these are assumed bases elements which allow us to obtain the numerical solutions of the singular boundary value problems. The obtained numerical results using this method are compared with the exact solution and existing methods (FDM, LWGM). Some of the problems are taken to demonstrate the applicability and validity of the proposed method.