Transforming Radical Differential Equations to Algebraic Differential Equations

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-04-02 DOI:10.1007/s00009-024-02624-1

Sebastian Falkensteiner, J. Rafael Sendra

引用次数: 0

Abstract

In this paper, we present an algorithmic procedure that transforms, if possible, a given system of ordinary or partial differential equations with radical dependencies in the unknown function and its derivatives into a system with polynomial relations among them by means of a rational change of variables. The solutions of the given equation and its transformation correspond one-to-one. This work can be seen as a generalization of previous work on reparametrization of ODEs and PDEs with radical coefficients.

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将根式微分方程转换为代数微分方程

在本文中，我们介绍了一种算法程序，该程序通过合理的变量变化，在可能的情况下，将未知函数及其导数具有根式依赖关系的给定常微分方程或偏微分方程系统转化为它们之间具有多项式关系的系统。给定方程的解与其变换一一对应。这项工作可以看作是对以前关于具有激元系数的 ODE 和 PDE 的重参数化工作的概括。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.