Numerical techniques for simulating a fractional mathematical model of epidermal wound healing

Chen, J., Liu, Fawang, Burrage, Kevin, & Shen, S. (2013) Numerical techniques for simulating a fractional mathematical model of epidermal wound healing. Journal of Applied Mathematics and Computing, 41(1-2), pp. 33-47.

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Abstract

A number of mathematical models investigating certain aspects of the complicated process of wound healing are reported in the literature in recent years. However, effective numerical methods and supporting error analysis for the fractional equations which describe the process of wound healing are still limited.

In this paper, we consider the numerical simulation of a fractional mathematical model of epidermal wound healing (FMM-EWH), which is based on the coupled advection-diffusion equations for cell and chemical concentration in a polar coordinate system. The space fractional derivatives are defined in the Left and Right Riemann-Liouville sense. Fractional orders in the advection and diffusion terms belong to the intervals (0, 1) or (1, 2], respectively. Some numerical techniques will be used. Firstly, the coupled advection-diffusion equations are decoupled to a single space fractional advection-diffusion equation in a polar coordinate system. Secondly, we propose a new implicit difference method for simulating this equation by using the equivalent of Riemann-Liouville and Grünwald-Letnikov fractional derivative definitions. Thirdly, its stability and convergence are discussed, respectively. Finally, some numerical results are given to demonstrate the theoretical analysis.

Impact and interest:

3 citations in Scopus
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ID Code: 59964
Item Type: Journal Article
Refereed: Yes
Keywords: Riesz fractional advection-dispersion equation, Epidermal wound healing, Polar coordinate system, Implicit finite difference approximation scheme, Stability, Convergence
DOI: 10.1007/s12190-012-0591-7
ISSN: 1865-2085
Divisions: Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2012 Korean Society for Computational and Applied Mathematics
Deposited On: 14 May 2013 00:10
Last Modified: 15 Jan 2014 14:36

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