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

Handle URI:
http://hdl.handle.net/10754/598359
Title:
Fourier spectral methods for fractional-in-space reaction-diffusion equations
Authors:
Bueno-Orovio, Alfonso; Kay, David; Burrage, Kevin
Abstract:
© 2014, Springer Science+Business Media Dordrecht. 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 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 reaction-diffusion equations described by the fractional Laplacian in bounded rectangular domains of ℝ. 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 illustrated 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.
Citation:
Bueno-Orovio A, Kay D, Burrage K (2014) Fourier spectral methods for fractional-in-space reaction-diffusion equations. Bit Numer Math 54: 937–954. Available: http://dx.doi.org/10.1007/s10543-014-0484-2.
Publisher:
Springer Nature
Journal:
BIT Numerical Mathematics
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
1-Apr-2014
DOI:
10.1007/s10543-014-0484-2
Type:
Article
ISSN:
0006-3835; 1572-9125
Sponsors:
This publication is based on work supported by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorBueno-Orovio, Alfonsoen
dc.contributor.authorKay, Daviden
dc.contributor.authorBurrage, Kevinen
dc.date.accessioned2016-02-25T13:19:21Zen
dc.date.available2016-02-25T13:19:21Zen
dc.date.issued2014-04-01en
dc.identifier.citationBueno-Orovio A, Kay D, Burrage K (2014) Fourier spectral methods for fractional-in-space reaction-diffusion equations. Bit Numer Math 54: 937–954. Available: http://dx.doi.org/10.1007/s10543-014-0484-2.en
dc.identifier.issn0006-3835en
dc.identifier.issn1572-9125en
dc.identifier.doi10.1007/s10543-014-0484-2en
dc.identifier.urihttp://hdl.handle.net/10754/598359en
dc.description.abstract© 2014, Springer Science+Business Media Dordrecht. 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 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 reaction-diffusion equations described by the fractional Laplacian in bounded rectangular domains of ℝ. 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 illustrated 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.en
dc.description.sponsorshipThis publication is based on work supported by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).en
dc.publisherSpringer Natureen
dc.subjectReaction-diffusion equationsen
dc.subjectFractional calculusen
dc.subjectFractional laplacianen
dc.subjectSpectral methodsen
dc.titleFourier spectral methods for fractional-in-space reaction-diffusion equationsen
dc.typeArticleen
dc.identifier.journalBIT Numerical Mathematicsen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
dc.contributor.institutionQueensland University of Technology QUT, Brisbane, Australiaen
kaust.grant.numberKUK-C1-013-04en
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