论文标题
在明确的两阶段四阶准确时间离散
On the explicit two-stage fourth-order accurate time discretizations
论文作者
论文摘要
本文继续研究显式两阶段的四阶准确时间离散[5，7]。通过引入可变的权重，我们提出了一类更通用的显式一步两阶段离散，这些分离与现有方法不同，例如Euler方法，Runge-Kutta方法以及多阶段的多阶段方法。我们研究了绝对稳定性，稳定性间隔以及绝对的Imiminaly Setborial and Sypection。我们的结果表明，我们的两个阶段时间离散可以是有条件准确的四阶准确性，具有可变权重的某些特殊选择的拟议方法的绝对稳定性区域可能大于经典的第四级或五阶runge-kutta方法的绝对稳定区域，并且绝对稳定性的间隔几乎可以是twice。进行了几个数值实验，以证明我们提出的方法的性能和准确性以及稳定性
This paper continues to study the explicit two-stage fourth-order accurate time discretiza- tions [5, 7]. By introducing variable weights, we propose a class of more general explicit one-step two-stage time discretizations, which are different from the existing methods, such as the Euler methods, Runge-Kutta methods, and multistage multiderivative methods etc. We study the absolute stability, the stability interval, and the intersection between the imaginary axis and the absolute stability region. Our results show that our two-stage time discretizations can be fourth-order accurate conditionally, the absolute stability region of the proposed methods with some special choices of the variable weights can be larger than that of the classical explicit fourth- or fifth-order Runge-Kutta method, and the interval of absolute stability can be almost twice as much as the latter. Several numerical experiments are carried out to demonstrate the performance and accuracy as well as the stability of our proposed methods
