Legendre-Gauss-Lobatto collocation method for solving multi-dimensional systems of mixed Volterra-Fredholm integral equations-Reference-Cited by-同舟云学术

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

Published:2023 Issue:9 Volume:8 Page:20871-20891
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Amin A. Z.¹,Abdelkawy M. A.²³,Amin Amr Kamel³⁴,Lopes António M.⁵,Alluhaybi Abdulrahim A.⁴,Hashim I.¹

Affiliation:

1. Department of Mathematical Sciences, Faculty of Science & Technology, Universiti Kebangsaan, Selangor, Malaysia

2. Department of Mathematics and Statistics, College of Science, Al-Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia

3. Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt

4. Department of Basic Sciences, Adham University College, Umm AL-Qura University, Makkah, Saudi Arabia

5. LAETA/INEGI, Faculty of Engineering, University of Porto, Porto, Portugal

Abstract

<abstract><p>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.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

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