Numerical Solution of Integral Equations Using Homotopy Perturbation Method and Series Solution Method

Abstract

The aim of this research paper is to develop numerical methods of solving linear Volterra integral equations using Homotopy Perturbation Method (HPM) and Series Solution Method (SSM). Most Integral equations are difficult to solve analytically, hence the need for a more accurate and reliably numerical method. In the the Homotopy Perturbation approach, the modelled problem is used to construct a homotopy and a perturbation expansion in terms of power series was assumed while in the series solution method, a power series solution was assumed and the assumed solution was substituted into the modelled problem by comparing the coefficient of like terms to obtain the unknown constants. The results of the two methods were compared and numerical examples were used to establish the simplicity, reliability and efficiency of the methods. The result shows that the methods are accurate and outperforms other methods existing in literature.