将根式微分方程转换为代数微分方程

IF 1.1 3区数学 Q1 MATHEMATICS Mediterranean Journal of Mathematics Pub Date : 2024-04-02 DOI:10.1007/s00009-024-02624-1

Sebastian Falkensteiner, J. Rafael Sendra

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引用次数: 0

摘要

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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Transforming Radical Differential Equations to Algebraic Differential Equations

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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来源期刊

Mediterranean Journal of Mathematics 数学-数学

CiteScore

1.80

自引率

0.00%

发文量

261

审稿时长

6-12 weeks

期刊介绍： The Mediterranean Journal of Mathematics (MedJM) is a publication issued by the Department of Mathematics of the University of Bari. The new journal replaces the Conferenze del Seminario di Matematica dell’Università di Bari which has been in publication from 1954 until 2003. The Mediterranean Journal of Mathematics aims to publish original and high-quality peer-reviewed papers containing significant results across all fields of mathematics. The submitted papers should be of medium length (not to exceed 20 printed pages), well-written and appealing to a broad mathematical audience. In particular, the Mediterranean Journal of Mathematics intends to offer mathematicians from the Mediterranean countries a particular opportunity to circulate the results of their researches in a common journal. Through such a new cultural and scientific stimulus the journal aims to contribute to further integration amongst Mediterranean universities, though it is open to contribution from mathematicians across the world.