A semi-alternating direction method for a 2-D fractional FitzHugh–Nagumo monodomain model on an approximate irregular domain

Liu, F., Zhuang, P., Turner, I., Anh, V., & Burrage, K. (2015) A semi-alternating direction method for a 2-D fractional FitzHugh–Nagumo monodomain model on an approximate irregular domain. Journal of Computational Physics, 293, pp. 252-263.

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Abstract

A FitzHugh-Nagumo monodomain model has been used to describe the propagation of the electrical potential in heterogeneous cardiac tissue. In this paper, we consider a two-dimensional fractional FitzHugh-Nagumo monodomain model on an irregular domain. The model consists of a coupled Riesz space fractional nonlinear reaction-diffusion model and an ordinary differential equation, describing the ionic fluxes as a function of the membrane potential. Secondly, we use a decoupling technique and focus on solving the Riesz space fractional nonlinear reaction-diffusion model. A novel spatially second-order accurate semi-implicit alternating direction method (SIADM) for this model on an approximate irregular domain is proposed. Thirdly, stability and convergence of the SIADM are proved. Finally, some numerical examples are given to support our theoretical analysis and these numerical techniques are employed to simulate a two-dimensional fractional Fitzhugh-Nagumo model on both an approximate circular and an approximate irregular domain.

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8 citations in Web of Science®

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ID Code: 82648
Item Type: Journal Article
Refereed: Yes
Additional URLs:
DOI: 10.1016/j.jcp.2014.06.001
ISSN: 0021-9991
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > APPLIED MATHEMATICS (010200) > Dynamical Systems in Applications (010204)
Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > NUMERICAL AND COMPUTATIONAL MATHEMATICS (010300) > Numerical Analysis (010301)
Divisions: Current > Research Centres > ARC Centre of Excellence for Mathematical & Statistical Frontiers (ACEMS)
Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2015 Elsevier
Copyright Statement: This is the author’s version of a work that was accepted for publication in Journal of Computational Physics. 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 Journal of Computational Physics, Vol 293, 2015, DOI: 10.1016/j.jcp.2014.06.001
Deposited On: 22 Mar 2015 23:44
Last Modified: 10 Aug 2015 05:45

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