Some Aspects of Numerical Analysis for a Model Nonlinear Fractional Variable Order Equation
The article proposes a nonlocal explicit finite-difference scheme for the numerical solution of a nonlinear, ordinary differential equation with a derivative of a fractional variable order of the Gerasimov–Caputo type. The questions of approximation, convergence, and stability of this scheme are stu...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2021-07-01
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| Series: | Mathematical and Computational Applications |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2297-8747/26/3/55 |
| Summary: | The article proposes a nonlocal explicit finite-difference scheme for the numerical solution of a nonlinear, ordinary differential equation with a derivative of a fractional variable order of the Gerasimov–Caputo type. The questions of approximation, convergence, and stability of this scheme are studied. It is shown that the nonlocal finite-difference scheme is conditionally stable and converges to the first order. Using the fractional Riccati equation as an example, the computational accuracy of the numerical method is analyzed. It is shown that with an increase in the nodes of the computational grid, the order of computational accuracy tends to unity, i.e., to the theoretical value of the order of accuracy. |
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| ISSN: | 1300-686X 2297-8747 |