| Autor: |
A.G. Omarova |
| Jazyk: |
English<br />Russian |
| Rok vydání: |
2024 |
| Předmět: |
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| Zdroj: |
Известия высших учебных заведений. Поволжский регион: Физико-математические науки, Iss 3 (2024) |
| Druh dokumentu: |
article |
| ISSN: |
2072-3040 |
| DOI: |
10.21685/2072-3040-2024-3-2 |
| Popis: |
Background. The object of study in this work is the Cauchy problem for an ordinary differential equation with the Riemann – Liouville fractional derivative on an interval [0,Т ]. A distinctive feature of the problem is that the order is a variable function α = α(t), that depends on time and satisfies the condition 0 < α(t) < 1. The purpose of the study is to construct a numerical method for solving the designated Cauchy problem. Materials and methods. For a numerical solution, the finite difference method is used, with the help of which the transition from a continuous region to a discrete one is carried out. A difference approximation of the Riemann – Liouville fractional derivative is used based on the definition of the Grunwald – Letnikov fractional derivative. Results. A difference scheme is constructed that approximates the original problem with order 2 − α(t) . The convergence and stability of the difference solution is proven. A computational experiment was also carried out for various functions α(t). Conclusions. The performed computational experiment confirms the convergence of the proposed method. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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