Affiliation of Author(s):数学学院

Journal:Journal of Computational Physics

Key Words:Space-fractional reaction-diffusion equations; Optimal error estimate; Semi-implicit time-stepping method; Fourier spectral method; Linear stability

Abstract:The reaction-diffusion model can generate a wide variety of spatial patterns, which has been widely applied in chemistry, biology, and physics, even used to explain self-regulated pattern formation in the developing animal embryo. In this work, a second-order stabilized semi-implicit time-stepping Fourier spectral method for the reaction-diffusion systems of equations with space described by the fractional Laplacian is developed. We adopt the temporal-spatial error splitting argument to illustrate that the proposed method is stable without imposing the CFL condition, and an optimal L-2-error estimate in space is proved. We also analyze the linear stability of the stabilized semi-implicit method and obtain a practical criterion to choose the time step size to guarantee the stability of the semi-implicit method. Our approach is illustrated by solving several problems of practical interest, including the fractional Allen-Cahn, Gray-Scott and FitzHugh-Nagumo models, together with an analysis of the properties of these systems in terms of the fractional power of the underlying Laplacian operator, which are quite different from the patterns of the corresponding integer-order model. (C) 2019 Elsevier Inc. All rights reserved.

All the Authors:George Em Karniadakis

First Author:zhanghui

Indexed by:Unit Twenty Basic Research

Correspondence Author:Jiang Xiaoyun,Fanhai Zeng

Discipline:Natural Science

First-Level Discipline:Mathematics

Volume:405

Page Number:109141

Translation or Not:no

Date of Publication:2020-03-01

Included Journals:SCI