Cost-reduction implicit exponential Runge–Kutta methods for highly oscillatory systems

IF 1.7 3区化学 Q3 CHEMISTRY, MULTIDISCIPLINARY

Journal of Mathematical Chemistry Pub Date : 2024-07-08 DOI:10.1007/s10910-024-01646-0

Xianfa Hu, Wansheng Wang, Bin Wang, Yonglei Fang

引用次数: 0

Abstract

In this paper, two novel classes of implicit exponential Runge–Kutta (ERK) methods are studied for solving highly oscillatory systems. First of all, symplectic conditions for two kinds of exponential integrators are derived, and we present a first-order symplectic method. High accurate implicit ERK methods (up to order four) are formulated by comparing the Taylor expansion of the exact solution, it is shown that the order conditions of two new kinds of exponential methods are identical to the order conditions of classical Runge–Kutta (RK) methods. Moreover, we investigate the linear stability properties of these exponential methods. Numerical examples not only present the long time energy preservation of the first-order symplectic method, but also illustrate the accuracy and efficiency of these formulated methods in comparison with standard ERK methods.

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高振荡系统的成本降低隐式指数 Runge-Kutta 方法

本文研究了用于求解高度振荡系统的两类新型隐式指数 Runge-Kutta (ERK) 方法。首先，推导了两种指数积分器的交映条件，并提出了一种一阶交映方法。通过比较精确解的泰勒展开，我们提出了高精度隐式 ERK 方法（最高四阶），并证明两种新指数方法的阶次条件与经典 Runge-Kutta (RK) 方法的阶次条件相同。此外，我们还研究了这些指数方法的线性稳定性。数值示例不仅展示了一阶交点法的长时间能量守恒，还说明了这些制定的方法与标准 ERK 方法相比的准确性和效率。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Mathematical Chemistry 化学-化学综合

CiteScore

3.70

自引率

17.60%

发文量

105

审稿时长

6 months

期刊介绍： The Journal of Mathematical Chemistry (JOMC) publishes original, chemically important mathematical results which use non-routine mathematical methodologies often unfamiliar to the usual audience of mainstream experimental and theoretical chemistry journals. Furthermore JOMC publishes papers on novel applications of more familiar mathematical techniques and analyses of chemical problems which indicate the need for new mathematical approaches. Mathematical chemistry is a truly interdisciplinary subject, a field of rapidly growing importance. As chemistry becomes more and more amenable to mathematically rigorous study, it is likely that chemistry will also become an alert and demanding consumer of new mathematical results. The level of complexity of chemical problems is often very high, and modeling molecular behaviour and chemical reactions does require new mathematical approaches. Chemistry is witnessing an important shift in emphasis: simplistic models are no longer satisfactory, and more detailed mathematical understanding of complex chemical properties and phenomena are required. From theoretical chemistry and quantum chemistry to applied fields such as molecular modeling, drug design, molecular engineering, and the development of supramolecular structures, mathematical chemistry is an important discipline providing both explanations and predictions. JOMC has an important role in advancing chemistry to an era of detailed understanding of molecules and reactions.