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Computational Methods for Solving Higher-Order (1+1) Dimensional Mixed-Difference Integro-Differential Equations with Variable Coefficients

Author

Listed:
  • Amr M. S. Mahdy

    (Department of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, Egypt
    Department of Mathematics & Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia)

  • Mohamed A. Abdou

    (Department of Mathematics, Faculty of Education, Alexandria University, Alexandria 21526, Egypt)

  • Doaa Sh. Mohamed

    (Department of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, Egypt)

Abstract

The main purpose of this article is to present a new technique for solving (1+1) mixeddimensional difference integro-differential Equations (2D-MDeIDEs) in position and time with coefficients of variables under mixed conditions. The equations proposed for the solution represent a link between time and delay in position that has not been previously studied. Therefore, the authors used the technique of separation of variables to transform the 2D-MDeIDE into one-dimensional Fredholm difference integro-differential Equations (FDeIDEs), and then using the Bernoulli polynomial method (BPM), we obtained a system of linear algebraic equations (SLAE). The other aspect of the technique of separation of variables is explicitly obtaining the necessary and appropriate time function to obtain the best numerical results. Some numerical experiments are performed to show the simplicity and efficiency of the presented method, and all results are performed by Maple 18.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:9:p:2045-:d:1132863
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    References listed on IDEAS

    as
    1. Faezeh Toutounian & Emran Tohidi & Stanford Shateyi, 2013. "A Collocation Method Based on the Bernoulli Operational Matrix for Solving High-Order Linear Complex Differential Equations in a Rectangular Domain," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-12, April.
    2. 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.
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