Numerical solution for singular differential equations using Haar wavelet

Abstract

The aim of this paper is to obtain the numerical solution of singular ordinary differential equations using the Haar-wavelet approach. The proposed method is mathematically simple and provides highly accurate solutions. In this method, we derive the Haar operational matrix using Haar function. Haar operational matrix is a basic tool and applied in system analysis to evaluate the numerical solution of differential equations. The convergence of the proposed method is discussed through its error analysis. To illustrate the efficiency of this method, solutions of four singular differential equations are obtained.