具有密度抑制运动的趋化系统无网格数值方法的收敛性

Federico Herrero-Herv'as, M. Negreanu, A. M. Vargas
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引用次数: 0

摘要

本文研究了一个抛物线-椭圆系统,模拟大肠杆菌对一种称为酰基高丝氨酸内酯浓度(AHL)的化学引诱剂的反应。该系统考虑了某些具有运动调节的细菌菌株,方程参数代表了细菌的logistic生长、AHL的扩散以及AHL的产生和降解速率。我们使用广义有限差分(GFD)方法来考虑系统的数值解,这是一种已知的有效计算非线性问题数值解的无网格方法。本文首先解释了该方法显式公式的推导,然后研究了显式格式的收敛性。然后给出了规则网格和不规则网格的算例。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Convergence of a meshless numerical method for a chemotaxis system with density-suppressed motility
This article studies a parabolic-elliptic system modelling the pattern formation in E. coli bacteria in response to a chemoattractant known as acylhomoserine lactone concentration (AHL). The system takes into account certain bacterial strains with motility regulation, and the parameters of the equations represent the bacterial logistic growth, AHL diffusion and the rates of production and degradation of AHL. We consider the numerical solution to the system using the Generalized Finite Difference (GFD) Method, a meshless method known to effectively compute numerical solutions to nonlinear problems. The paper is organized to first explain the derivation of the explicit formulae of the method, followed by the study of the convergence of the explicit scheme. Then, several examples over regular and irregular meshes are given.
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