A Nonoscillatory Second-Order Time-Stepping Procedure for Reaction-Diffusion Equations
A Nonoscillatory Second-Order Time-Stepping Procedure for Reaction-Diffusion Equations
复制标题
反应扩散方程的非振荡二阶时间步进过程
DOI：
10.1155/2020/5163704
复制
发表时间：
2020
期刊：
影响因子：
2.3
通讯作者：
Kim, Seongjai
中科院分区：
文献类型：
--
作者：
Lee, Philku;Popescu, George V.;Kim, Seongjai
自20世纪50年代提出细胞形态发生理论以来，反应扩散偏微分方程组(PDE)的数值解引起了人们的广泛关注。克朗克-尼科尔森(CN)方法是一种常见的二阶时间步长方法。然而，除非时间步长足够小，否则CN方法可能会对非光滑数据引入虚假振荡。本文研究了一种求解RD方程的非振荡二阶时间步长方法，称为Avariable-θ方法，作为CN方法的摄动。在每个时间层中，新方法检测潜在振荡点，以隐式地求解那里的解。所提出的时间步进过程是无振荡的，并且具有二阶时间精度。给出了各种算例，说明了该方法的有效性。本文还对生物格局形成模型的数值解进行了敏感性分析，得出数值解对空间网格分辨率比时间网格分辨率敏感得多的结论。随着精度的提高而提高空间分辨率，CN方法可能会产生虚假振荡，而所提出的方法会得到稳定的解。
After a theory of morphogenesis in chemical cells was introduced in the 1950s, much attention had been devoted to the numerical solution ofreaction-diffusion(RD)partial differential equations(PDEs). TheCrank–Nicolson(CN) method has been a common second‐order time‐stepping procedure. However, the CN method may introduce spurious oscillations for nonsmooth data unless the time step size is sufficiently small. This article studies a nonoscillatory second‐order time‐stepping procedure for RD equations, called avariable-θmethod, as a perturbation of the CN method. In each time level, the new method detects points of potential oscillations to implicitly resolve the solution there. The proposed time‐stepping procedure is nonoscillatory and of a second‐order temporal accuracy. Various examples are given to show effectiveness of the method. The article also performs a sensitivity analysis for the numerical solution of biological pattern forming models to conclude that the numerical solution is much more sensitive to the spatial mesh resolution than the temporal one. As the spatial resolution becomes higher for an improved accuracy, the CN method may produce spurious oscillations, while the proposed method results in stable solutions.
影响因子：
2.4
作者：
I. Sgura;B. Bozzini;D. Lacitignola
通讯作者：
D. Lacitignola
DOI：
--
发表时间：
2006
期刊：
影响因子：
--
作者：
J. Douglas;Seongjai Kim;Hyeona Lim
通讯作者：
Hyeona Lim
影响因子：
1.6
作者：
Philku Lee;T. Kim;Seongjai Kim
通讯作者：
Seongjai Kim