Title: A new approach based on generalised multiquadric and compactly supported radial basis functions for solving two-dimensional Volterra-Fredholm integral equations

Authors: Dalila Takouk; Rebiha Zeghdane; Belkacem Lakehali

Addresses: Department of Mathematics, Faculty of Mathematics and Informatics, University of Bordj-Bou-Arreridj, Algeria ' Department of Mathematics, Faculty of Mathematics and Informatics, University of Bordj-Bou-Arreridj, Algeria ' Department of Mathematics, Faculty of Mathematics and Informatics, University of Msila, Algeria

Abstract: This article describes a numerical scheme to solve two-dimensional nonlinear Volterra-Fredholm integral equations (IEs). The method estimates the solution by compactly supported radial basis functions and compared with the approximation of the solution by generalised multiquadric radial basis function with the optimal strategy for the exponent β. Integrals appearing in the procedure of the solution are approximated using shifted Legendre-Gauss-Lobatto nodes and weights. The method is mathematically simple and truly meshless. It can be used for high-dimensional problems because it does not require any cell structures. Finally, numerical experiments are given to show and test the applicability of the presented approach and confirm the theoretical analysis.

Keywords: Volterra-Fredholm integral equations; two-dimensional integral equations; generalised multiquadric radial basis functions; compactly supported radial basis functions; interpolation method; shifted Legendre-Gauss-Lobatto nodes and weights.

DOI: 10.1504/IJCSE.2022.126257

International Journal of Computational Science and Engineering, 2022 Vol.25 No.5, pp.532 - 547

Received: 02 Apr 2021
Accepted: 18 Sep 2021
Published online: 18 Oct 2022 *

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