An implicit Keller Box numerical scheme for the solution of fractional subdiffusion equations
Article
Osman, S. A and Langlands, T. A. M.. 2019. "An implicit Keller Box numerical scheme for the solution of fractional subdiffusion equations." Applied Mathematics and Computation. 348, pp. 609-626. https://doi.org/10.1016/j.amc.2018.12.015
| Article Title | An implicit Keller Box numerical scheme for the solution of fractional subdiffusion equations |
|---|---|
| ERA Journal ID | 49 |
| Article Category | Article |
| Authors | Osman, S. A (Author) and Langlands, T. A. M. (Author) |
| Journal Title | Applied Mathematics and Computation |
| Journal Citation | 348, pp. 609-626 |
| Number of Pages | 18 |
| Year | 2019 |
| Place of Publication | United States |
| ISSN | 0096-3003 |
| 1873-5649 | |
| Digital Object Identifier (DOI) | https://doi.org/10.1016/j.amc.2018.12.015 |
| Web Address (URL) | https://www.sciencedirect.com/science/article/pii/S0096300318310622 |
| Abstract | In this work, we present a new implicit numerical scheme for fractional subdiffusion equations. In this approach we use the Keller Box method [1] to spatially discretise the fractional subdiffusion equation and we use a modified L1 scheme (ML1), similar to the L1 scheme originally developed by Oldham and Spanier [2], to approximate the fractional derivative. The stability of the proposed method was investigated by using Von-Neumann stability analysis. We have proved the method is unconditionally stable when 0<λq<min([Formula presented],2γ) and 0 < γ ≤ 1, and demonstrated the method is also stable numerically in the case [Formula presented]<λq≤2γ and log32 ≤ γ ≤ 1. The accuracy and convergence of the scheme was also investigated and found to be of order O(Δt1+γ) in time and O(Δx2) in space. To confirm the accuracy and stability of the proposed method we provide three examples with one including a linear reaction term. |
| Keywords | fractional subdiffusion equation, Keller Box method, fractional calculus, L1 scheme, linear reaction |
| ANZSRC Field of Research 2020 | 490303. Numerical solution of differential and integral equations |
| Public Notes | File reproduced in accordance with the copyright policy of the publisher/author. |
| Byline Affiliations | School of Agricultural, Computational and Environmental Sciences |
| Computational Engineering and Science Research Centre | |
| Institution of Origin | University of Southern Queensland |
| Funding source | Australian Research Council (ARC) Grant ID DP130100595 |
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