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

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 a...

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Bibliographic Details
Published in:Mathematics (Basel) 2023-04, Vol.11 (9), p.2045
Main Authors: Mahdy, Amr M. S., Abdou, Mohamed A., Mohamed, Doaa Sh
Format: Article
Language:English
Subjects:
Algebra
Analysis
Bernoulli polynomials
Boundary conditions
collocation point
Decomposition
difference integro-differential equations
Differential equations
Integral equations
Linear algebra
Mathematics
Methods
Numerical analysis
Polynomials
Separation
separation of variables
Time functions
Variables
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math11092045