纯粹四分法和用概率演化理论求解常微分方程，同时用精确算术计算系数

IF 1.7 3区化学 Q3 CHEMISTRY, MULTIDISCIPLINARY Journal of Mathematical Chemistry Pub Date : 2023-12-30 DOI:10.1007/s10910-023-01563-8

Coşar Gözükırmızı

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摘要

概率演化理论为具有多项式右侧函数的常微分方程的求解提供了一种很有前途的方法。本研究用 C++ 编程语言实现了概率演化理论的求解方法。设计并实现了一种并发计算序列展开系数的新算法。通过使用该程序，获得了不同常微分方程的近似解，并将结果与某些著名的常微分方程数值解法的结果进行了比较。

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Pure quadratization and solution of ordinary differential equations by probabilistic evolution theory with concurrent computation of coefficients using exact arithmetic

Probabilistic evolution theory provides a promising method for the solution of ordinary differential equations with multinomial right hand side functions. In this work, the solution by probabilistic evolution theory is implemented in C++ programming language. A novel algorithm for concurrent computation of the coefficients of the series expansion is designed and implemented. Using the program, approximate solutions for different ordinary differential equations are obtained and the results are compared to results of certain prominent methods for numerical solution of ordinary differential equations.

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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.