Cai, L., Guo, M., Li, Y., Ying, W., Gao, H. and Luo, X. (2019) Nonstandard finite difference method for nonlinear Riesz space fractional reaction-diffusion equation. International Journal of Numerical Analysis and Modeling, 16(6), pp. 925-938.
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Publisher's URL: http://www.global-sci.com/intro/article_detail/ijnam/13260.html
Abstract
In this paper, a modified nonstandard finite difference method for the two-dimensional Riesz space fractional reaction-diffusion equations is developed. The space fractional derivative is discretized by the shifted Grünwald-Letnikov method and the nonlinear reaction term is approximated by Taylor formula instead of Micken’s. Multigrid method is introduced to reduce the computation time of the traditional Gauss-Seidal method. The stability and convergence of the nonstandard implicit difference scheme are strictly proved. The method is extended to simulate the fractional FitzHugh-Nagumo model. Numerical results are provided to verify the theoretical analysis.
| Item Type: | Articles |
|---|---|
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Luo, Professor Xiaoyu and Gao, Dr Hao and Cai, Dr Li |
| Authors: | Cai, L., Guo, M., Li, Y., Ying, W., Gao, H., and Luo, X. |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics |
| Journal Name: | International Journal of Numerical Analysis and Modeling |
| Publisher: | Global Science Press |
| ISSN: | 1705-5105 |
| ISSN (Online): | 1705-5105 |
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