论文标题
Runge-Kutta框架中的投射集成方法和时间适应性的扩展
Projective Integration Methods in the Runge-Kutta Framework and the Extension to Adaptivity in Time
论文作者
论文摘要
投影整合方法是具有较大光谱差距的刚性ODE的明确时间集成方案。在本文中，我们表明所有现有的投射集成方法都可以写为runge-kutta方法，其中包含许多阶段，包括扩展的屠夫图表。我们使用Runge-Kutta框架证明了投射集成方法的一致性和顺序条件。通过分区的runge-kutta方法包括在空间自适应的投射集成方法。新的时间自适应投影集成方案是通过嵌入式runge-kutta方法和步长尺寸变化得出的，而其准确性，稳定性，收敛性和误差估计器进行了分析和数值研究。
Projective Integration methods are explicit time integration schemes for stiff ODEs with large spectral gaps. In this paper, we show that all existing Projective Integration methods can be written as Runge-Kutta methods with an extended Butcher tableau including many stages. We prove consistency and order conditions of the Projective Integration methods using the Runge-Kutta framework. Spatially adaptive Projective Integration methods are included via partitioned Runge-Kutta methods. New time adaptive Projective Integration schemes are derived via embedded Runge-Kutta methods and step size variation while their accuracy, stability, convergence, and error estimators are investigated analytically and numerically.
