P. Kim
127 Vincent Hall, 206 Church St. S.E.,, MN 55455, Minneapolis, United States of America
Department of Mathematics, University of Minnesota, Minneapolis, Minnesota
Publications:
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Kim P., Olver P. J.
Geometric integration via multi-space
2004, vol. 9, no. 3, pp. 213-226
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.
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