High order symplectic partitioned Lie group methods
For researchers in geometric numerical integration, this provides a general framework to derive high-order symplectic integrators for Lie group systems, though it is an incremental extension of existing methods.
This paper presents a unified approach to construct symplectic integrators on the cotangent bundle of a Lie group from Lie group integrators, achieving arbitrarily high order. The approach is demonstrated for Runge-Kutta-Munthe-Kaas and Crouch-Grossman methods.
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.