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所属单位：数学学院

发表刊物：Journal of Computational Physics

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

摘要：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.

全部作者：George Em Karniadakis

第一作者：张慧

论文类型：基础研究

通讯作者：蒋晓芸,曾凡海

学科门类：理学

一级学科：数学

卷号：405

页面范围：109141

是否译文：否

发表时间：2020-03-01

收录刊物：SCI