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Two-Dimensional Fredholm Integro-Differential Equation with Singular Kernel and Its Numerical Solutions

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  • Abeer M. Al-Bugami
  • Su Yan

Abstract

In this paper, we introduce the nonlinear Fredholm integro-differential equation of the second kind with singular kernel in two-dimensional NT-DFIDE. Furthermore, we study this new equation numerically. The existence of a unique solution of the equation is proved. The numerical results of NT-DFIDE are obtained by the following methods: Toeplitz matrix method (TMM) and product Nystrom method (PNM). The given applications showed the efficiency of these methods.

Suggested Citation

  • Abeer M. Al-Bugami & Su Yan, 2022. "Two-Dimensional Fredholm Integro-Differential Equation with Singular Kernel and Its Numerical Solutions," Advances in Mathematical Physics, Hindawi, vol. 2022, pages 1-8, December.
    • Handle: RePEc:hin:jnlamp:2501947
    DOI: 10.1155/2022/2501947
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    Cited by:

    1. Amr M. S. Mahdy & Mohamed A. Abdou & Doaa Sh. Mohamed, 2023. "Computational Methods for Solving Higher-Order (1+1) Dimensional Mixed-Difference Integro-Differential Equations with Variable Coefficients," Mathematics, MDPI, vol. 11(9), pages 1-25, April.

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