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Research Article | Open Access

Legendre-Gauss-Lobatto collocation method for solving multi-dimensional systems of mixed Volterra-Fredholm integral equations

A. Z. Amin1, M. A. Abdelkawy2,3, Amr Kamel Amin3,4, António M. Lopes5( ), Abdulrahim A. Alluhaybi4, I. Hashim1
Department of Mathematical Sciences, Faculty of Science & Technology, Universiti Kebangsaan, Selangor, Malaysia
Department of Mathematics and Statistics, College of Science, Al-Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia
Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt
Department of Basic Sciences, Adham University College, Umm AL-Qura University, Makkah, Saudi Arabia
LAETA/INEGI, Faculty of Engineering, University of Porto, Porto, Portugal
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Abstract

Integral equations play a crucial role in many scientific and engineering problems, though solving them is often challenging. This paper addresses the solution of multi-dimensional systems of mixed Volterra-Fredholm integral equations (SMVF-IEs) by means of a Legendre-Gauss-Lobatto collocation method. The one-dimensional case is addressed first. Afterwards, the method is extended to two-dimensional linear and nonlinear SMVF-IEs. Several numerical examples reveal the effectiveness of the approach and show its superiority in comparison to other alternative techniques for treating SMVF-IEs.

Keywords

system of mixed Volterra-Fredholm integral equationsspectral collocation methodshifted Legendre polynomialsshifted Legendre-Gauss-Lobatto quadrature
CLC number: 45Dxx, 65Mxx, 44-XX

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AIMS Mathematics
Volume 8 Issue 9,
September 2023
Pages 20871-20891
DOI: 10.3934/math.20231063

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Cite this article:
Amin AZ, Abdelkawy MA, Amin AK, et al. Legendre-Gauss-Lobatto collocation method for solving multi-dimensional systems of mixed Volterra-Fredholm integral equations. AIMS Mathematics, 2023, 8(9): 20871-20891. https://doi.org/10.3934/math.20231063

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Received: 22 February 2023
Revised: 15 June 2023
Accepted: 20 June 2023
Published: 15 September 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)