127 Vincent Hall, 206 Church St. S.E.,, MN 55455, Minneapolis, United States of America
Department of Mathematics, University of Minnesota, Minneapolis, Minnesota
Kim P., Olver P. J.
Geometric integration via multi-space
2004, vol. 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.