Numerical treatment of a two-dimensional variable-order fractional nonlinear reaction-diffusion model

Liu, Fawang, Zhuang, Pinghui, Turner, Ian, Anh, Vo, & Burrage, Kevin (2014) Numerical treatment of a two-dimensional variable-order fractional nonlinear reaction-diffusion model. In Baleanu, Dumitru & Tenreiro Machado, Jose A. (Eds.) ICFDA 2014 International Conference on Fractional Differentiation and its Applications, IEEE, Catania, Sicily, Italy, pp. 1-6.

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Abstract

A two-dimensional variable-order fractional nonlinear reaction-diffusion model is considered. A second-order spatial accurate semi-implicit alternating direction method for a two-dimensional variable-order fractional nonlinear reaction-diffusion model is proposed. Stability and convergence of the semi-implicit alternating direct method are established. Finally, some numerical examples are given to support our theoretical analysis. These numerical techniques can be used to simulate a two-dimensional variable order fractional FitzHugh-Nagumo model in a rectangular domain. This type of model can be used to describe how electrical currents flow through the heart, controlling its contractions, and are used to ascertain the effects of certain drugs designed to treat arrhythmia.

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ID Code: 84638
Item Type: Conference Paper
Refereed: Yes
Additional URLs:
Keywords: Variable-order operator, Alternating direction method, Second-order spacial accuracy, Fractional nonlinear reaction-diffusion model, Stability and convergence
DOI: 10.1109/ICFDA.2014.6967430
ISBN: 9781479925919
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000)
Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > NUMERICAL AND COMPUTATIONAL MATHEMATICS (010300)
Divisions: Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2014 IEEE
Copyright Statement: Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Deposited On: 02 Jun 2015 23:54
Last Modified: 06 Jun 2015 07:30

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