Fourier spectral method for higher order space fractional reaction-diffusion equations
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Date
Authors
Pindza, Edson
Owolabi, Kolade M.
Journal Title
Journal ISSN
Volume Title
Publisher
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.
Description
Keywords
Fractional exponential integrators, Fourier transform, Fractional reaction-diffusion system, Pattern formation, Turing instability
Sustainable Development Goals
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.