A Taylor expansion approach using Faà di Bruno's formula for solving nonlinear integral equations of the second and third kind

Abstract

Purpose

The purpose of this paper is to present a method for solving nonlinear integral equations of the second and third kind.

Design/methodology/approach

The method converts the nonlinear integral equation into a system of nonlinear equations. By solving the system, the solution can be determined. Comparing the methodology with some known techniques shows that the present approach is simple, easy to use, and highly accurate.

Findings

The proposed technique allows the authors to obtain an approximate solution in a series form. Test problems are given to illustrate the pertinent features of the method. The accuracy of the numerical results indicates that the technique is efficient and well‐suited for solving nonlinear integral equations.

Originality/value

The present approach provides a reliable technique that avoids the difficulties and massive computational work if compared with the traditional techniques and does not require discretization in order to find solutions to the given problems.

Citation

Ben Zitoun, F. and Cherruault, Y. (2009), "A Taylor expansion approach using Faà di Bruno's formula for solving nonlinear integral equations of the second and third kind", Kybernetes, Vol. 38 No. 5, pp. 800-818. https://doi.org/10.1108/03684920910962687