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An Analytical Approach to Solve a System of 2D Nonlinear Volterra–Fredholm Integral Equations on Nonrectangular Domains Based on Radial Basis Functions

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  • Mohsen Jalalian
  • Manochehr Kazemi
  • Mohammad Esmael Samei

Abstract

We aim to introduce a numerical method to solve a system of two-dimensional nonlinear integral equations of Volterra–Fredholm type with the second kind on nonrectangular domains. The method estimates the solutions of the system by a discrete collocation method based on radial basis functions constructed on scattered points. The proposed technique is meshless because it does not require any domain elements, making it independent of the geometry of the domain. This approach simplifies the solution of the system of the solution of a nonlinear system of algebraic equations. The convergence of the algorithm is discussed rigorously. In conclusion, some illustrative examples are numerically presented to demonstrate the efficiency of the mentioned numerical methods.

Suggested Citation

  • Mohsen Jalalian & Manochehr Kazemi & Mohammad Esmael Samei, 2025. "An Analytical Approach to Solve a System of 2D Nonlinear Volterra–Fredholm Integral Equations on Nonrectangular Domains Based on Radial Basis Functions," Journal of Mathematics, Hindawi, vol. 2025, pages 1-22, October.
    • Handle: RePEc:hin:jjmath:9934661
    DOI: 10.1155/jom/9934661
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