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

dc.contributor.authorPindza, Edson
dc.contributor.authorOwolabi, Kolade M.
dc.date.accessioned2016-08-11T06:58:38Z
dc.date.issued2016-11
dc.description.abstractEvolution 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.departmentMathematics and Applied Mathematicsen_ZA
dc.description.embargo2017-11-30
dc.description.librarianhb2016en_ZA
dc.description.urihttp://www.elsevier.com/locate/cnsnsen_ZA
dc.identifier.citationPindza, 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.issn1007-5704 (print)
dc.identifier.issn1878-7274 (online)
dc.identifier.other10.1016/j.cnsns.2016.04.020
dc.identifier.urihttp://hdl.handle.net/2263/56262
dc.language.isoenen_ZA
dc.publisherElsevieren_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.subjectFractional exponential integratorsen_ZA
dc.subjectFourier transformen_ZA
dc.subjectFractional reaction-diffusion systemen_ZA
dc.subjectPattern formationen_ZA
dc.subjectTuring instabilityen_ZA
dc.titleFourier spectral method for higher order space fractional reaction-diffusion equationsen_ZA
dc.typePostprint Articleen_ZA

Files

Original bundle

Now showing 1 - 1 of 1
Loading...
Thumbnail Image
Name:
Pindza_Fourier_2016.pdf
Size:
1.42 MB
Format:
Adobe Portable Document Format
Description:
Postprint Article

License bundle

Now showing 1 - 1 of 1
Loading...
Thumbnail Image
Name:
license.txt
Size:
1.75 KB
Format:
Item-specific license agreed upon to submission
Description: