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
收藏
页码：213 / 226
页数：14
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