Numerical investigation of two models of nonlinear fractional reaction subdiffusion equations
Article
Osman, Sheelan and Langlands, Trevor. 2022. "Numerical investigation of two models of nonlinear fractional reaction subdiffusion equations." Fractional Calculus and Applied Analysis. 25 (6), pp. 2166-2192. https://doi.org/10.1007/s13540-022-00096-2
| Article Title | Numerical investigation of two models of nonlinear fractional reaction subdiffusion equations |
|---|---|
| ERA Journal ID | 39668 |
| Article Category | Article |
| Authors | Osman, Sheelan (Author) and Langlands, Trevor (Author) |
| Journal Title | Fractional Calculus and Applied Analysis |
| Journal Citation | 25 (6), pp. 2166-2192 |
| Number of Pages | 27 |
| Year | 2022 |
| Place of Publication | Germany |
| ISSN | 1311-0454 |
| Digital Object Identifier (DOI) | https://doi.org/10.1007/s13540-022-00096-2 |
| Web Address (URL) | https://link.springer.com/article/10.1007/s13540-022-00096-2 |
| Abstract | We consider new numerical schemes to solve two different systems of nonlinear fractional reaction subdiffusion equations. These systems of equations model the reversible reaction A+B⇌C in the presence of anomalous subdiffusion. The first model is based on the Henry \& Wearne [1] model where the reaction term is added to the subdiffusion equation. The second model is based on the model by Angstmann, Donnelly \& Henry [2] which involves a modified fractional differential operator. For both models the Keller Box method [3] along with a modified L1 scheme (ML1), adapted from the Oldham and Spanier L1 scheme [4], are used to approximate the spatial and fractional derivatives respectively. Numerical prediction of both models were compared for a number of examples given the same initial and boundary conditions and the same anomalous exponents. From the results, we see similar short time behaviour for both models predicted. However for long times the solution of the second model remains positive whilst the Henry \& Wearne based–model predictions may become negative. |
| Keywords | Fractional reaction subdiffusion equation; Keller Box method; Fractional calculus; L1 scheme; Nonlinear reactions systems |
| ANZSRC Field of Research 2020 | 490299. Mathematical physics not elsewhere classified |
| 490303. Numerical solution of differential and integral equations | |
| 490199. Applied mathematics not elsewhere classified | |
| Byline Affiliations | Soran University, Iraq |
| School of Sciences | |
| Institution of Origin | University of Southern Queensland |
| Funding source | Australian Research Council (ARC) Grant ID ARC120 DP130100595 |
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