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Numerical simulation of a fractional mathematical model for epidermal wound healing

Chen, J., Liu, F., Burrage, K., & Shen, S. (2012) Numerical simulation of a fractional mathematical model for epidermal wound healing. In Chen, Wen, Sun, HongGuang, & Baleanu, Dumitru (Eds.) Proceedings of the 5th Symposium on Fractional Differentiation and Its Applications, Hohai University, Hohai University, Nanjing.

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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 numerical simulation of fractional model 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 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 the Riemann-Liouville and Gr¨unwald-Letnikov fractional derivative definitions.

Thirdly, its stability and convergence are discussed, respectively.

Finally, some numerical results are given to demonstrate the theoretical analysis.

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ID Code: 51461
Item Type: Conference Paper
Keywords: Riesz fractional advection-dispersion equation, polar coordinate system, implicit finite difference approximation scheme, stability, convergence
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000)
Australian and New Zealand Standard Research Classification > ENGINEERING (090000)
Divisions: Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2012 [please consult the author]
Deposited On: 09 Jul 2012 09:06
Last Modified: 13 Jul 2013 07:46

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