We apply geometric integrators of the RKMK type to the problem of numerically integrating Lie-Poisson systems. By using the coadjoint action of the Lie group G on the dual Lie algebra g^* to advance the numerical flow, we devise methods of arbritrary order that automatically stay on the coadjoint orbits. First integrals known as Casimirs are retained to machine accuracy by the numerical algorithm. Within the proposed class of methods we find integrators that also conserve the energy exactly. These schemes are implicit and of second order. Numerical experiments are used to illustrate the properties of the algorithm.

MINISIMPOSIUM SESSION: 12. Lie Group methods