Volume 16, Issue 6
Nonstandard Finite Difference Method for Nonlinear Riesz Space Fractional Reaction-Diffusion Equation

Li Cai ,  Meifang Guo ,  Yiqiang Li ,  Wenjun Ying ,  Hao Gao and Xiaoyu Luo

Int. J. Numer. Anal. Mod., 16 (2019), pp. 925-938.

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  • 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.

  • History

Published online: 2019-08

  • AMS Subject Headings

65M06, 65M12

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