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dc.contributor.authorBueno-Orovio, Alfonso
dc.contributor.authorKay, David
dc.contributor.authorBurrage, Kevin
dc.date.accessioned2016-02-25T13:19:21Z
dc.date.available2016-02-25T13:19:21Z
dc.date.issued2014-04-01
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.
dc.identifier.issn0006-3835
dc.identifier.issn1572-9125
dc.identifier.doi10.1007/s10543-014-0484-2
dc.identifier.urihttp://hdl.handle.net/10754/598359
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.
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).
dc.publisherSpringer Nature
dc.subjectReaction-diffusion equations
dc.subjectFractional calculus
dc.subjectFractional laplacian
dc.subjectSpectral methods
dc.titleFourier spectral methods for fractional-in-space reaction-diffusion equations
dc.typeArticle
dc.identifier.journalBIT Numerical Mathematics
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdom
dc.contributor.institutionQueensland University of Technology QUT, Brisbane, Australia
kaust.grant.numberKUK-C1-013-04
dc.date.published-online2014-04-01
dc.date.published-print2014-12


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