ARTICLE
The numerical methods for solving of the one-dimensional anomalous reaction-diffusion equation
1
Silesian University of Technology, Department of Mathematics Applications and Methods for Artificial Intelligence, Poland
Submission date: 2023-12-27
Final revision date: 2024-02-12
Acceptance date: 2024-02-19
Online publication date: 2024-04-13
Publication date: 2024-04-30
Corresponding author
Marek Błasik
Department of Mathematics Applications and Methods for Artificial Intelligence, Silesian University of Technology, Poland
Department of Mathematics Applications and Methods for Artificial Intelligence, Silesian University of Technology, Poland
Journal of Theoretical and Applied Mechanics 2024;62(2):365-376
KEYWORDS
fractional derivatives and integralsintegro-differential equationsnumericalmethodsanomalous diffusion
TOPICS
ABSTRACT
This paper presents numerical methods for solving the one-dimensional fractional reaction-
-diffusion equation with the fractional Caputo derivative. The proposed methods are based
on transformation of the fractional differential equation to an equivalent form of a integro-
-differential equation. The paper proposes an improvement of the existing implicit method,
and a new explicit method. Stability and convergence tests of the methods were also con-
ducted.
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| eISSN: | 2543-6309 |
| ISSN: | 1429-2955 |
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