论文标题
分数步骤runge - kutta方法：表示和线性稳定性分析
Fractional-Step Runge--Kutta Methods: Representation and Linear Stability Analysis
论文作者
论文摘要
分数步骤方法是用于微分方程的数值解决方案的流行且强大的分裂方法。当分数步骤的集成器是runge的 - kutta方法时，可以将这种方法写成通用的添加剂runge-kutta（gark）方法，因此可以通过Gark框架来完成此类方法的表示和分析。我们展示了此类方法的一般屠夫图表表示和线性稳定性如何与分裂方法的系数，单个子集成剂及其应用的顺序有关。我们使用此框架来解释有关分数方法的文献中的一些观察结果，例如选择子积分器的选择，应用程序的顺序以及负面分裂系数在该方法稳定性中所起的作用。
Fractional-step methods are a popular and powerful divide-and-conquer approach for the numerical solution of differential equations. When the integrators of the fractional steps are Runge--Kutta methods, such methods can be written as generalized additive Runge--Kutta (GARK) methods, and thus the representation and analysis of such methods can be done through the GARK framework. We show how the general Butcher tableau representation and linear stability of such methods are related to the coefficients of the splitting method, the individual sub-integrators, and the order in which they are applied. We use this framework to explain some observations in the literature about fractional-step methods such as the choice of sub-integrators, the order in which they are applied, and the role played by negative splitting coefficients in the stability of the method.
