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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

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, 2022. "Two‐Dimensional Fredholm Integro‐Differential Equation with Singular Kernel and Its Numerical Solutions," Advances in Mathematical Physics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jnlamp:v:2022:y:2022:i:1:n:2501947
    DOI: 10.1155/2022/2501947
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    1. Z. Pashazadeh Atabakan & A. Kazemi Nasab & A. Kılıçman, 2013. "On Solution of Fredholm Integrodifferential Equations Using Composite Chebyshev Finite Difference Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. Z. Pashazadeh Atabakan & A. Kazemi Nasab & A. Kılıçman, 2013. "On Solution of Fredholm Integrodifferential Equations Using Composite Chebyshev Finite Difference Method," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-11, June.
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