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.
Original language | English (US) |
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Pages (from-to) | 213-226 |
Number of pages | 14 |
Journal | Regular and Chaotic Dynamics |
Volume | 9 |
Issue number | 3 |
DOIs | |
State | Published - 2004 |