Nonstandard Finite Difference Method for Nonlinear Riesz Space Fractional Reaction-Diffusion Equation

Authors

  • Li Cai NPU-UoG International Cooperative Lab for Computation & Application in Cardiology, Northwestern Polytechnical University, Xi’an, Shaanxi, 710072, P.R.China
  • Meifang Guo NPU-UoG International Cooperative Lab for Computation & Application in Cardiology, Northwestern Polytechnical University, Xi’an, Shaanxi, 710072, P.R.China
  • Yiqiang Li NPU-UoG International Cooperative Lab for Computation & Application in Cardiology, Northwestern Polytechnical University, Xi’an, Shaanxi, 710072, P.R.China
  • Wenjun Ying School of Mathematical Sciences and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai, 200240, P.R.China
  • Hao Gao School of Mathematics and Statistics, University of Glasgow, University Gardens, Glasgow, G12 8QW, UK
  • Xiaoyu Luo School of Mathematics and Statistics, University of Glasgow, University Gardens, Glasgow, G12 8QW, UK

Keywords:

Riesz fractional derivative, nonstandard finite difference method, shifted Grünwald-Letnikov method.

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.

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Published

2019-08-09

Issue

Vol. 16 No. 6 (2019)

Section

Articles