期刊
BIT NUMERICAL MATHEMATICS
卷 54, 期 4, 页码 937-954出版社
SPRINGER
DOI: 10.1007/s10543-014-0484-2
关键词
Fractional calculus; Fractional laplacian; Spectral methods; Reaction-diffusion equations
资金
- King Abdullah University of Science and Technology (KAUST) [KUK-C1-013-04]
Fractional differential equations are becoming increasingly used as a powerful modelling approach for understanding the many aspects of nonlocality and spatial heterogeneity. However, the numerical approximation of these models is demanding and imposes a number of computational constraints. In this paper, we introduce Fourier spectral methods as an attractive and easy-to-code alternative for the integration of fractional-in-space reaction-diffusion equations described by the fractional Laplacian in bounded rectangular domains of . The main advantages of the proposed schemes is that they yield a fully diagonal representation of the fractional operator, with increased accuracy and efficiency when compared to low-order counterparts, and a completely straightforward extension to two and three spatial dimensions. Our approach is illustrated by solving several problems of practical interest, including the fractional Allen-Cahn, FitzHugh-Nagumo and Gray-Scott models, together with an analysis of the properties of these systems in terms of the fractional power of the underlying Laplacian operator.
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