Geometric integration via multi-space

P. Kim, P. J. Olver

Research output: Contribution to journalArticlepeer-review

33 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)213-226
Number of pages14
JournalRegular and Chaotic Dynamics
Issue number3
StatePublished - 2004


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