High order symplectic partitioned Lie group methods
Numerical Analysis
2014-04-24 v3
Abstract
In this article, a unified approach to obtain symplectic integrators on T*G from Lie group integrators on a Lie group G is presented. The approach is worked out in detail for symplectic integrators based on Runge--Kutta--Munthe-Kaas methods and Crouch--Grossman methods. These methods can be interpreted as symplectic partitioned Runge--Kutta methods extended to the Lie group setting in two different ways. In both cases, we show that it is possible to obtain symplectic integrators of arbitrarily high order by this approach.
Cite
@article{arxiv.1303.5654,
title = {High order symplectic partitioned Lie group methods},
author = {Geir Bogfjellmo and Håkon Marthinsen},
journal= {arXiv preprint arXiv:1303.5654},
year = {2014}
}
Comments
33 pages, 3 figures; major improvements and corrections after peer review