Title: A rational spectral collocation method for solving Fredholm integral equations on the whole line
Authors: Azedine Rahmoune; Ahmed Guechi
Addresses: Faculty of Mathematics and Computer Sciences, LPMRN Laboratory, Department of Mathematics, University of Bordj Bou Arreridj, El Anasser, 34030, Algeria ' Faculty of Mathematics and Computer Sciences, LPMRN Laboratory, Department of Mathematics, University of Bordj Bou Arreridj, El Anasser, 34030, Algeria
Abstract: In this paper, a numerical method is proposed to solve a class of linear Fredholm integral equations on the whole line. The method is developed by means of mapped Gegenbauer rational functions. A special quadrature rule based on mapped Gegenbauer-Gauss points and weights is then utilised to evaluate the infinite integrals appeared in the scheme. Thus, the solution of the problem reduces to the solution of a simple system of algebraic equations. Convergence and error analysis are discussed and numerical examples illustrate the efficiency of the method.
Keywords: mapped Gegenbauer rational approximation; Fredholm integral equations; the whole line; collocation method; stability.
International Journal of Computing Science and Mathematics, 2021 Vol.13 No.1, pp.32 - 41
Received: 18 Nov 2019
Accepted: 03 Feb 2020
Published online: 13 Apr 2021 *