代数-几何方法:用参数化法求解代数微分方程

IF 2 3区数学 Q1 MATHEMATICS

Bulletin of the American Mathematical Society Pub Date : 2022-07-11 DOI:10.1090/bull/1773

Sebastian Falkensteiner, Johann J. Mitteramskogler, J. Sendra, F. Winkler

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引用次数: 2

摘要

我们综述了通过相关代数集的参数化来求解代数常微分方程的代数几何方法。特别地，我们处理一阶方程，以及代数几何维一的系统。对各类解进行符号化处理，如有理解、代数解和幂级数解。我们还考虑了保留微分方程解的相关代数集的代数变换类。介绍了两个Maple包，实现了其中一些解决方案方法。

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The algebro-geometric method: Solving algebraic differential equations by parametrizations

We present a survey of the algebro-geometric method for solving algebraic ordinary differential equations by means of parametrizations of the associated algebraic sets. In particular, we deal with equations of order one, and also systems of algebro-geometric dimension one. Various classes of solutions are treated symbolically, such as rational, algebraic, and power series solutions. We also consider classes of algebraic transformations of the associated algebraic sets preserving the solutions of the differential equations. Two Maple packages, implementing some of these solution methods, are presented.

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来源期刊

Bulletin of the American Mathematical Society 数学-数学

CiteScore

2.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.