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

Amr M. S. Mahdy (), Mohamed A. Abdou and Doaa Sh. Mohamed
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Amr M. S. Mahdy: Department of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, Egypt
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

Mathematics, 2023, vol. 11, issue 9, 1-25

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.

Keywords: difference integro-differential equations; separation of variables; Bernoulli polynomials; collocation point (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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