TY - JOUR
T1 - Nonstandard Finite Difference Method for Nonlinear Riesz Space Fractional Reaction-Diffusion Equation
AU - Cai , Li
AU - Guo , Meifang
AU - Li , Yiqiang
AU - Ying , Wenjun
AU - Gao , Hao
AU - Luo , Xiaoyu
JO - International Journal of Numerical Analysis and Modeling
VL - 6
SP - 925
EP - 938
PY - 2019
DA - 2019/08
SN - 16
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/13260.html
KW - Riesz fractional derivative, nonstandard finite difference method, shifted Grünwald-Letnikov method.
AB - <p style="text-align: justify;">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&#39;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.</p>