求解径向Schrödinger方程的新型指数拟合二阶龙格-库塔方法

IF 1.7 3区化学 Q3 CHEMISTRY, MULTIDISCIPLINARY

Journal of Mathematical Chemistry Pub Date : 2024-11-06 DOI:10.1007/s10910-024-01681-x

Yonglei Fang, Hengmin Lv, Xiong You

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引用次数: 0

摘要

本文给出了一类新的指数阶为2的指数拟合二阶龙格-库塔（TDRK）方法，用于求解Schrödinger方程。根据能量的渐近表达式进行误差分析。分析了其线性稳定性和相特性。数值结果表明，与一些专门针对径向时间无关Schrödinger方程与Woods-Saxon势的积分的RK型方法相比，新方法具有效率和鲁棒性。

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Novel exponentially fitted two-derivative Runge–Kutta methods for solving the radial Schrödinger equation

A family of new exponentially fitted two-derivative Runge–Kutta (TDRK) methods with exponential order up to two for solving the Schrödinger equation is obtained in this paper. Error analysis is conducted in terms of the asymptotic expressions of the energy. Linear stability and phase properties are analyzed. Numerical results are reported to show the efficiency and robustness of the new methods in comparison with some RK type methods specially tuned to the integration of the radial time-independent Schrödinger equation with the Woods-Saxon potential.

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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.