A numerical comparative analysis of methods for solving fractional differential equations
| Autor: | Syeda Tehmina Ejaz, Namra Zulqarnain, Jihad Younis, Saima Bibi |
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| Jazyk: | angličtina |
| Rok vydání: | 2024 |
| Předmět: | |
| Zdroj: | Arab Journal of Basic and Applied Sciences, Vol 31, Iss 1, Pp 154-164 (2024) |
| Druh dokumentu: | article |
| ISSN: | 25765299 2576-5299 |
| DOI: | 10.1080/25765299.2024.2314379 |
| Popis: | In this paper, we present two collocation methods utilizing subdivision schemes and Bernstein polynomials as their basis functions to solve Caputo-type fractional differential equations. These methods transform fractional differential equations into systems of linear equations, which can be solved using various suitable techniques. Notably, these methods are versatile, making them applicable to both boundary value problems and initial value problems. To demonstrate their effectiveness, we applied these methods to three test problems of fractional differential equations, including the Bagley-Torvik equation and fractional oscillation equation. Our results reveal that both methods provide a more accurate approximation to the exact solution when compared to various algorithms found in the existing literature, showcasing their efficiency, accuracy, and consistency. |
| Databáze: | Directory of Open Access Journals |
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