A numerical approach for solving first order integro-differential equations

Abstract

A polynomial spline of degree n is made up of polynomial segments of degree n that are connected in a way that guarantees the continuity of the function and of its derivatives up to order n-1. This paper presents a numerical method based on cubic spline function with a free boundary condition for the solution of first order integro-differential equations. The solution procedure of this technique is simple and straightforward. Several test examples are considered to demonstrate the applicability and performance of the method. The results obtained by the proposed method are compared with the exact solutions and some existing results in literatures.