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

中文翻译：

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关于显式两阶段四阶精确时间离散化

本文继续研究显式两阶段四阶精确时间离散[5, 7]。通过引入可变权重，我们提出了一类更通用的显式一步两阶段时间离散，它们不同于现有的方法，如欧拉方法、龙格-库塔方法和多阶段多导数方法等。我们研究了绝对稳定、稳定区间、虚轴与绝对稳定区域的交点。我们的结果表明，我们的两阶段时间离散化可以有条件地达到四阶精度，具有一些特殊的可变权重选择的方法的绝对稳定区域可以大于经典显式四阶或五阶龙格的绝对稳定区域-库塔方法，而绝对稳定的区间几乎可以是后者的两倍。进行了一些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