Partitioned Runge-Kutta methods in Lie-group setting

We introduce partitioned Runge-Kutta (PRK) methods as geometric integrators in the Runge-Kutta-Munthe-Kaas (RKMK) method hierarchy. T his is done by first noticing that tangent and cotangent bundles are the natural domains for the differential equations to be solved. Next, we equip the (co)tangent bundle of a Lie group with a group structure and treat it as a Lie group. The structure of the differential equations on the (co)tangent-bundle Lie group is such that partitioned versions of the RKMK methods are naturally introduced. Numerical examples are included to illustrate the new methods.