A first-rate fourteenth-order phase-fitting approach to solving chemical problems

IF 1.7 3区化学 Q3 CHEMISTRY, MULTIDISCIPLINARY

Journal of Mathematical Chemistry Pub Date : 2024-09-17 DOI:10.1007/s10910-024-01668-8

Mei Hong, Chia-Liang Lin, T. E. Simos

引用次数: 0

Abstract

Using a technique that accounts for disappearing phase-lag might lead to the elimination of phase-lag and all of its derivatives up to order four. The new technique known as the cost-efficient approach aims to improve algebraic order (AOR) and decrease function evaluations (FEvs). The one-of-a-kind approach is shown by Equation PF4DPHFITN142SPS. This method is endlessly periodic since it is P-Stable. The proposed method may be used to solve many different types of periodic and/or oscillatory problems. This innovative method was used to address the difficult issue of Schrödinger-type coupled differential equations in quantum chemistry. The new technique might be seen as a cost-efficient solution since it only requires 5FEvs to execute each step. We are able to greatly ameliorate our current situation with an AOR of 14.

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解决化学问题的一流十四阶相位拟合方法

使用一种考虑到相位滞后消失的技术，可能会消除相位滞后及其所有导数，最高可达四阶。这种被称为 "成本效益方法 "的新技术旨在改善代数阶（AOR）和减少函数求值（FEvs）。这种独一无二的方法如公式 PF4DPHFITN142SPS 所示。由于这种方法是 P-稳定的，因此它具有无穷无尽的周期性。所提出的方法可用于解决许多不同类型的周期和/或振荡问题。这种创新方法被用于解决量子化学中薛定谔型耦合微分方程的难题。新技术可被视为一种经济高效的解决方案，因为它只需要 5FEvs 就能执行每一步。我们能够以 14 的 AOR 大大改善目前的状况。

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.