Paper Publications
A stabilized semi-implicit Fourier spectral method for nonlinear space-fractional reaction-diffusion equations
Release Time:2020-07-14
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Institution:
数学学院
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Journal:
Journal of Computational Physics
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Key Words:
Space-fractional reaction-diffusion equations; Optimal error estimate; Semi-implicit time-stepping method; Fourier spectral method; Linear stability
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Summary:
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.
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First Author:
张慧
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Correspondence Author:
Jiang Xiaoyun,Fanhai Zeng
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All the Authors:
George Em Karniadakis
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Discipline:
Natural Science
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First-Level Discipline:
Mathematics
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Volume:
405
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Page Number:
109141
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Translation or Not:
No
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Date of Publication:
2020-03
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Included Journals:
SCI
