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Numerical simulation of a fractional mathematical model for epidermal wound healing

机译：表皮伤口愈合的分数数学模型的数值模拟

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摘要

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 Grünwald-Letnikov fractional derivative de.nitions. Thirdly, its stability and convergence are discussed, respectively. Finally, some numerical results are given to demonstrate the theoretical analysis.
机译：近年来，文献报道了许多研究复杂伤口愈合过程某些方面的数学模型。然而，用于描述伤口愈合过程的分数方程的有效数值方法和辅助误差分析仍然有限。在本文中，我们考虑基于极坐标系中细胞和化学物浓度的耦合对流扩散方程的分数模型的数值模拟。空间分数导数以左和右黎曼-利维尔的意义定义。对流和扩散项的分数阶分别属于区间（0; 1）或（1; 2]，将使用一些数值技术：首先，将耦合的对流扩散方程解耦为单个空间分数对流扩散极坐标系中的方程，其次，我们提出了一种新的隐式差分方法，利用Riemann-Liouville和Grünwald-Letnikov分数阶导数的等价物来模拟该方程，其次讨论了其稳定性和收敛性。最后，给出了一些数值结果来证明理论分析。

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