10.57647/

The Combined Reproducing Kernel Method and Taylor Series for Solving Nonlinear Volterra-Fredholm Integro-Differential Equations

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  • A Alvandi1,
  • M Paripour2,
  1. Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran.
  2. Department of Computer Engineering and Information Technology, Hamedan University of Technology, Hamedan, 65155-579, Iran.

Received: 15-08-2016

Revised: 18-10-2016

Accepted: 20-11-2016

Published in Issue 28-07-2025

Copyright (c) 2025 A Alvandi, M Paripour (Author)

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This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Alvandi, A., & Paripour, M. (2025). The Combined Reproducing Kernel Method and Taylor Series for Solving Nonlinear Volterra-Fredholm Integro-Differential Equations. International Journal of Mathematical Modelling & Computations, 6(4). https://doi.org/10.57647/
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Abstract

In this paper, the numerical scheme of nonlinear Volterra-Fredholm integrodifferential equations is proposed in a reproducing kernel Hilbert space (RKHS). The method is constructed based on the reproducing kernel properties in which the initial condition of the problem is satisfied. The nonlinear terms are replaced by its Taylor series. In this technique, the nonlinear Volterra-Fredholm integro-differential equations are converted to nonlinear differential equations. The exact solution is represented in the form of series in the reproducing Hilbert kernel space. The approximation solution is expressed by n-term summation of reproducing kernel functions and it is converge to the exact solution. Some numerical examples are given to show the accuracy of the method.

Keywords

  • Reproducing kernel method,
  • Volterra-Fredholm integro-differential equations,
  • Approximation solution
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