A compact discretization of the boundary value problems of the nonlinear Fredholm integro-differential equations

Amiri, Sadegh; Hajipour, Mojtaba

doi:10.22124/jmm.2023.24380.2184

A compact discretization of the boundary value problems of the nonlinear Fredholm integro-differential equations

Document Type : Research Article

Authors

Sadegh Amiri ¹
Mojtaba Hajipour ²

¹ Department of Basic Sciences, Shahid Sattari Aeronautical University of Science and Technology, P.O. Box: 13846-63113, Tehran, Iran

² Department of Mathematics, Sahand University of Technology, P.O. Box: 51335-1996, Tabriz, Iran

10.22124/jmm.2023.24380.2184

Abstract

In this paper, we propose a fourth-order compact discretization method for solving a second-order boundary value problem governed by the nonlinear Fredholm integro-differential equations. Using an efficient approximate polynomial, a compact numerical integration method is first designed. Then by applying the derived numerical integration formulas, the original problem is converted into a nonlinear system of algebraic equations. It is shown that the proposed method is easy to implement and has the third order of accuracy in the infinity norm. Some numerical examples are presented to demonstrate its approximation accuracy and computational efficiency, as well as to compare the derived results with those obtained in the literature.

Keywords