An Approximate Solution of Non-Linear System of Volterra Integral Equation

Burhan F J Al-Salehi

doi:10.33899/csmj.2008.163945

Abstract

A Taylor series expansion is developed and applied to evaluate an approximate solution of the non-linear system of Volterra integral equation of the second kind for both Urysohn and Hammerstein types. The solution is based on substituting for the unknown function after differentiating both sides of the integral equation. Program associated with above methods is written in Matlab, finally, by using various examples, the accuracy of this method will be shown.

Highlights

Integral equations appear in many engineering and physics, Numerical methods of solution for integral equations have been largely developed in the last 20 years [3,7]
Al-Faour used Taylor series expansion to evaluate the approximate solution of linear system of integral equations for Volterra type [2]
(t, u j (t ))dt i = 1,2,..., n where kij(s,t) and fi(s) are known functions. This system appear in many applications for instance: the Dirichelt-Neumann mixed boundary value problems (MBVPs) on closed surfaces in R3 based on an equivalent formulation of the MBVP as a system of two integral equations [7]

Summary

Introduction

Integral equations appear in many engineering and physics, Numerical methods of solution for integral equations have been largely developed in the last 20 years [3,7]. Al-Faour used Taylor series expansion to evaluate the approximate solution of linear system of integral equations for Volterra type [2]. The main purpose of this paper is to consider Taylor series expansion of non-linear system of Volterra integral equation for Urysohn (SNLUVIEs) and Hammerstein (SNLHVIEs) types of the form ns ui (s) =

Objectives

Results

Conclusion