Effective numerical technique for solving variable order integro-differential equations

In this article, an effective numerical technique for solving the variable order Fredholm–Volterra integro-differential equations (VO-FV-IDEs), systems of VO-FV-IDEs and variable order Volterra partial integro-differential equations (VO-V-PIDEs) is given. The suggested technique is built on the comb...

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Bibliographic Details
Published in:Journal of applied mathematics & computing 2022-08, Vol.68 (4), p.2823-2855
Main Authors: El-Gindy, Taha M., Ahmed, Hoda F., Melad, Marina B.
Format: Article
Language:English
Subjects:
Applied mathematics
Collocation methods
Computational Mathematics and Numerical Analysis
Differential equations
Mathematical analysis
Mathematical and Computational Engineering
Mathematics
Mathematics and Statistics
Mathematics of Computing
Numerical methods
Original Research
Polynomials
Theory of Computation
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Summary:In this article, an effective numerical technique for solving the variable order Fredholm–Volterra integro-differential equations (VO-FV-IDEs), systems of VO-FV-IDEs and variable order Volterra partial integro-differential equations (VO-V-PIDEs) is given. The suggested technique is built on the combination of the spectral collocation method with some types of operational matrices of the variable order fractional differentiation and integration of the shifted fractional Gegenbauer polynomials (SFGPs). The proposed technique reduces the considered problems to systems of algebraic equations that are straightforward to solve. The error bound estimation of using SFGPs is discussed. Finally, the suggested technique’s authenticity and efficacy are tested via presenting several numerical applications. Comparisons between the outcomes achieved by implementing the proposed method with other numerical methods in the existing literature are held, the obtained numerical results of these applications reveal the high precision and performance of the proposed method.
ISSN:1598-5865
1865-2085
DOI:10.1007/s12190-021-01640-8