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Local meshless method for PDEs arising from models of wound healing

机译:伤口愈合模型产生的局部无网格PDEs方法

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摘要

A meshless collocation procedure is proposed for one- and two-dimensional partial differential equations arising from modeling of wound healing processes (Sherratt and Murray, 1991). Main motivation of this choice is its straightforward application in higher dimensions for both regular and irregular domains on various nodal points distributions. In the case of numerical solution of convection-dominated wound healing PDE models, a stencil based upwind stabilization technique is coupled with the local meshless method to counter instabilities of the computed solution. To assess efficacy, efficiency and accuracy of the proposed method on regular and irregular domains, numerical approximations of different wound healing models are obtained and validated against the exact solution and medically tested healing time duration.
机译:针对伤口愈合过程的建模所产生的一维和二维偏微分方程,提出了一种无网格搭配程序(Sherratt and Murray,1991)。这种选择的主要动机是将其直接应用在各种节点点分布上的规则和不规则域的更高维度中。在以对流为主的伤口愈合PDE模型的数值解的情况下,将基于模板的迎风稳定技术与局部无网格方法相结合,以抵消所计算解的不稳定性。为了评估所提出方法在规则和不规则域上的功效,效率和准确性,获得了不同伤口愈合模型的数值近似值,并针对确切的解决方案和经过医学测试的愈合时间进行了验证。

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