10.30495/ijm2c.2023.1960582.1254

A Numerical Solution for 2D-Nonlinear Fredholm Integral Equations Based on Hybrid Functions Basis

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  • Maryam Mohammadi1,
  • A. Zakeri*2,
  • Majid Karami3,
  • Narges Taheri3,
  • Raheleh Nouraei3,
  1. Islamic Azad University, South Tehran Branch, Tehran
  2. Khajeh Nasir Toosi University of Technology
  3. Islamic Azad University, South Tehran Branch

Received: 08-06-2022

Accepted: 02-04-2023

Published in Issue 01-03-2023

Copyright (c) 2024 International Journal of Mathematical Modeling & Computations

Creative Commons License

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

How to Cite

Mohammadi, M., Zakeri, A., Karami, M., Taheri, N., & Nouraei, R. (2023). A Numerical Solution for 2D-Nonlinear Fredholm Integral Equations Based on Hybrid Functions Basis. International Journal of Mathematical Modelling & Computations, 13(1), 0-0. https://doi.org/10.30495/ijm2c.2023.1960582.1254
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Abstract

This work considers a numerical method based on the 2D-hybrid block-pulse functions and normalized Bernstein polynomials to solve 2D-nonlinear Fredholm integral equations of the second type. These problems are reduced to a system of nonlinear algebraic equations and solved by Newton's iterative method along with the numerical integration and collocation methods. Also, the convergence theorem for this algorithm is proved. Finally, some numerical examples are given to show the effectiveness and simplicity of the proposed method.

Keywords

  • collocation method, Fredholm integral equations, Convergence analysis, Bivariate hybrid block-pulse functions, Normalized Bernstein polynomials
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