Geometric integration via multi-space
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- Geometric integration via multi-space
- Kim, Pilwon; Olver, PJ
- Issue Date
- MAIK NAUKA/INTERPERIODICA/SPRINGER
- REGULAR & CHAOTIC DYNAMICS, v.9, no.3, pp.213 - 226
- 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.
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