The Mathematical Institute, University of Oxford, Eprints Archive

Fourier spectral methods for fractional-in-space reaction-diffusion equations

Bueno-Orovio, A. and Kay, D. and Burrage, K. (2012) Fourier spectral methods for fractional-in-space reaction-diffusion equations. Journal of Computational Physics . (Submitted)

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Abstract

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 computationally 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 reactiondiffusion equations. 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 show-cased 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.

Item Type:Article
Subjects:D - G > General
Research Groups:Oxford Centre for Collaborative Applied Mathematics
ID Code:1551
Deposited By:Peter Hudston
Deposited On:05 Jul 2012 08:50
Last Modified:05 Jul 2012 08:50

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