Fourier spectral method for higher order space fractional reaction-diffusion equations
dc.contributor.author | Pindza, Edson | |
dc.contributor.author | Owolabi, Kolade M. | |
dc.date.accessioned | 2016-08-11T06:58:38Z | |
dc.date.issued | 2016-11 | |
dc.description.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. | en_ZA |
dc.description.department | Mathematics and Applied Mathematics | en_ZA |
dc.description.embargo | 2017-11-30 | |
dc.description.librarian | hb2016 | en_ZA |
dc.description.uri | http://www.elsevier.com/locate/cnsns | en_ZA |
dc.identifier.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. | en_ZA |
dc.identifier.issn | 1007-5704 (print) | |
dc.identifier.issn | 1878-7274 (online) | |
dc.identifier.other | 10.1016/j.cnsns.2016.04.020 | |
dc.identifier.uri | http://hdl.handle.net/2263/56262 | |
dc.language.iso | en | en_ZA |
dc.publisher | Elsevier | en_ZA |
dc.rights | © 2016 Elsevier. All rights reserved. Notice : this is the author’s version of a work that was accepted for publication in Communications in Nonlinear Science and Numerical Simulation. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Communications in Nonlinear Science and Numerical Simulation, vol. 40, no. 11, pp. 112-128, 2016. doi : 10.1016/j.cnsns.2016.04.020. | en_ZA |
dc.subject | Fractional exponential integrators | en_ZA |
dc.subject | Fourier transform | en_ZA |
dc.subject | Fractional reaction-diffusion system | en_ZA |
dc.subject | Pattern formation | en_ZA |
dc.subject | Turing instability | en_ZA |
dc.title | Fourier spectral method for higher order space fractional reaction-diffusion equations | en_ZA |
dc.type | Postprint Article | en_ZA |