@Article{IJNAM-16-6,
author = {Li, Cai and Meifang, Guo and Yiqiang, Li and Ying, Wenjun and Hao, Gao and Xiaoyu, Luo},
title = {Nonstandard Finite Difference Method for Nonlinear Riesz Space Fractional Reaction-Diffusion Equation},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2019},
volume = {16},
number = {6},
pages = {925--938},
abstract = {<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>},
issn = {2617-8710},
doi = {https://doi.org/2019-IJNAM-13260},
url = {https://global-sci.com/article/83084/nonstandard-finite-difference-method-for-nonlinear-riesz-space-fractional-reaction-diffusion-equation}
}