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• W2935707000 endingPage "109141" @default.
• W2935707000 startingPage "109141" @default.
• W2935707000 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 is presented for the reaction-diffusion systems of equations with space described by the fractional Laplacian. We adopt the temporal-spatial error splitting argument to illustrate that the proposed method is stable without imposing the CFL condition, and we prove an optimal L2-error estimate. 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." @default.
• W2935707000 created "2019-04-25" @default.
• W2935707000 creator A5003759585 @default.
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• W2935707000 date "2020-03-01" @default.
• W2935707000 modified "2023-10-14" @default.
• W2935707000 title "A stabilized semi-implicit Fourier spectral method for nonlinear space-fractional reaction-diffusion equations" @default.
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• W2935707000 doi "https://doi.org/10.1016/j.jcp.2019.109141" @default.
• W2935707000 hasPublicationYear "2020" @default.
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