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This article is cited in 34 scientific papers (total in 34 papers)
Effective computations in modern dynamics
Geometric integration via multi-space
P. Kim, P. J. Olver Department of Mathematics,
University of Minnesota,
MN 55455, USA
Abstract:
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.
Received: 20.08.2004
Citation:
P. Kim, P. J. Olver, “Geometric integration via multi-space”, Regul. Chaotic Dyn., 9:3 (2004), 213–226
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https://www.mathnet.ru/eng/rcd743 https://www.mathnet.ru/eng/rcd/v9/i3/p213
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Abstract page: | 93 |
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