A numerical method based on the radial basis functions for solving nonlinear two-dimensional Volterra integral equations of the second kind on non-rectangular domains

Document Type : Research Article

Authors

1 Department of Mathematics, Ilam University, P.O. Box 69315516, Ilam, Iran

2 Department of Mathematics, College of Education ,University of Garmian, Kurdistan Region-Iraq

3 Department of Mathematics, College of Education, University of Garmian, Kurdistan Region-Iraq

4 Faculty of Humanities, Islamic Azad University, Ilam Branch, Ilam, Iran

Abstract

In this investigation, a numerical method for solving nonlinear two-dimensional Volterra integral equations is presented. This method uses radial basis functions (RBFs) constructed on scattered points as a basis in the discrete collocation method. Therefore, the method does not need any background mesh or cell structure of the domain. All the integrals that appear in this method are approximated by the composite Gauss-Legendre integration formula. This method transforms the source problem into a system of nonlinear algebraic equations. Error analysis is presented for this method. Finally, numerical examples are included to show the validity and efficiency of this technique.

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Journal of Mathematical Modeling
Volume 12, Issue 4
December 2024
Pages 687-705

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