Krylov implicit integration factor method for a class of stiff reaction-diffusion systems with moving boundaries
Krylov implicit integration factor method for a class of stiff reaction-diffusion systems with moving boundaries
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DOI：
10.3934/dcdsb.2019176
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Shuang Liu;Xinfeng Liu
中科院分区：
文献类型：
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作者：
Shuang Liu;Xinfeng Liu
反应扩散方程组与由Stefan条件定义的移动边界耦合已被广泛用于描述种群扩散动力学。要有效地处理这样的系统，有几个数值上的困难。首先，由于系统的刚度，通常要求极小的时间步长。其次，如何高效、准确地处理移动边界一直是一个难题。为了克服这些困难，我们首先将具有移动边界的一维问题转化为具有固定计算域的系统，然后引入四种不同的时间格式：Runge-Kutta， Crank-Nicolson，隐式积分因子（IIF）和Krylov IIF来处理这类刚性系统。数值算例说明了不同方法的效率、准确性和一致性，并通过直接比较表明，Krylov IIF在稳定性和效率方面优于其他三种方法。
The systems of reaction-diffusion equations coupled with moving boundaries defined by Stefan condition have been widely used to describe the dynamics of spreading population. There are several numerical difficulties to efficiently handle such systems. Firstly extremely small time steps are usually demanded due to the stiffness of the system. Secondly it is always difficult to efficiently and accurately handle the moving boundaries. To overcome these difficulties, we first transform the one-dimensional problem with a moving boundary into a system with a fixed computational domain, and then introduce four different temporal schemes: Runge-Kutta, Crank-Nicolson, implicit integration factor (IIF) and Krylov IIF for handling such stiff systems. Numerical examples are examined to illustrate the efficiency, accuracy and consistency for different approaches, and it can be shown that Krylov IIF is superior to other three approaches in terms of stability and efficiency by direct comparison.