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Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations
- Publisher
- Springer Journals
- Copyright
- Copyright © Korean Society for Informatics and Computational Applied Mathematics 2021
- ISSN
- 1598-5865
- eISSN
- 1865-2085
- DOI
- 10.1007/s12190-021-01640-8
- Publisher site
- See Article on Publisher Site
Abstract
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.
Journal
Journal of Applied Mathematics and Computing – Springer Journals
Published: Aug 1, 2022
Keywords: Distinct kinds of variable order integro-differential equations; Shifted fractional Gegenbauer polynomials; Operational matrices; Collocation method; 34A08; 33C45; 65M70