@Article{IJNAM-16-925, author = {Cai , LiGuo , MeifangLi , YiqiangYing , WenjunGao , Hao and Luo , Xiaoyu}, 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 = {

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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/13260.html} }