Fourier spectral method for higher order space fractional reaction-diffusion equations

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Authors

Pindza, Edson
Owolabi, Kolade M.

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Elsevier

Abstract

Evolution equations containing fractional derivatives can provide suitable mathemati- cal models for describing important physical phenomena. In this paper, we propose a fast and accurate method for numerical solutions of space fractional reaction-diffusion equations. The proposed method is based on a exponential integrator scheme in time and the Fourier spectral method in space. The main advantages of this method are that it yields a fully diagonal representation of the fractional operator, with increased accuracy and efficiency, and a completely straightforward extension to high spatial di- mensions. Although, in general, it is not obvious what role a high fractional derivative can play and how to make use of arbitrarily high-order fractional derivatives, we in- troduce them to describe fractional hyper-diffusions in reaction diffusion. The scheme justified by a number of computational experiments, this includes two and three dimen- sional partial differential equations. Numerical experiments are provided to validate the effectiveness of the proposed approach.

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Keywords

Fractional exponential integrators, Fourier transform, Fractional reaction-diffusion system, Pattern formation, Turing instability

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Citation

Pindza, E & Owolabi, KM 2016, 'Fourier spectral method for higher order space fractional reaction-diffusion equations', Communications in Nonlinear Science and Numerical Simulation, vol. 40, no. 1, pp. 112-128.