10.30495/ijm2c.2022.688969

Numerical Solution Two-Dimensional Volterra-Fredholm Integral Equations of the Second Kind with Block-Pulse Functions Based on Legendre Polynomials

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  • Jafar Khazaian1,
  • Nouredin Parandin*2,
  • Farajollah Mohammadi Yaghoobi3,
  • Nasrin Karami Kabir1,
  1. Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran.
  2. Department of Mathematics Kermanshah Branch, Islamic Azad University, Kermanshah, Iran
  3. Department of Mathematics Hamedan Branch, Islamic Azad University Hamedan, Iran.

Received: 02-03-2021

Accepted: 08-02-2022

Published in Issue 30-03-2022

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

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

How to Cite

Khazaian, J., Parandin, N., Mohammadi Yaghoobi, F., & Karami Kabir, N. (2022). Numerical Solution Two-Dimensional Volterra-Fredholm Integral Equations of the Second Kind with Block-Pulse Functions Based on Legendre Polynomials. International Journal of Mathematical Modelling & Computations, 12(1), 1-14. https://doi.org/10.30495/ijm2c.2022.688969
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Abstract

In this paper, we present a new numerical technique based on Block-pulse functions to solve two-dimensional Volterra-Fredholm integral equations of the second kind. To produce Block-pulse functions, the orthogonal Legendre polynomials is used. Furthermore, operational matrix is applied to convert two-dimensional Volterra-Fredholm integral equations to a linear algebraic system. The convergence analysis of the new method is discussed. Finally, some numerical examples are given to confirm the applicability and efficiency of the new method for solving two-dimensional Volterra-Fredholm integral equations of the second kind.
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