Geometric integration via multi-space

被引：32

作者：

Kim, P ^{[1
]}

Olver, PJ ^{[1
]}

机构：

[1] Univ Minnesota, Dept Math, Minneapolis, MN 55455 USA

来源：

REGULAR & CHAOTIC DYNAMICS | 2004年 / 9卷 / 03期

关键词：

D O I：

10.1070/RD2004v009n03ABEH000277

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We outline a general construction of symmetry-preserving numerical schemes for ordinary differential equations. The method of invariantization is based on the equivariant moving frame theory applied to prolonged symmetry group actions on multi-space, which has been proposed as the proper geometric setting for numerical analysis. We explain how to invariantize standard numerical integrators such as the Euler and Runge-Kutta schemes; in favorable situations, the resulting symmetry-preserving geometric integrators offer significant advantages.

引用

页码：213 / 226

页数：14

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