High order symplectic partitioned Lie group methods

Understand

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.