Nonstandard Finite Difference Method for Nonlinear Riesz Space Fractional Reaction-Diffusion Equation
Year: 2019
Author: Li Cai, Meifang Guo, Yiqiang Li, Wenjun Ying, Hao Gao, Xiaoyu Luo
International Journal of Numerical Analysis and Modeling, Vol. 16 (2019), Iss. 6 : pp. 925–938
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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2019-IJNAM-13260
International Journal of Numerical Analysis and Modeling, Vol. 16 (2019), Iss. 6 : pp. 925–938
Published online: 2019-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 14
Keywords: Riesz fractional derivative nonstandard finite difference method shifted Grünwald-Letnikov method.