Study implementation issues for Lie group integrators and invariant preserving integrators. Results will include: 1) Variable step size Lie group integrators with error control; 2) Invariant preserving schemes for mechanical systems evolving on Riemannian manifolds; 3) Model reduction applied to large dynamical systems on Lie groups and manifolds.

New software generation for Lie group integration to be used for concrete applications from THREAD. For Lie group integrators with stepwise updated local coordinates standard error control from integrators on linear spaces can be applied. There is no such direct reference to coordinate charts for composition based Lie group integrators making them more tricky to work with (order conditions for non-commutative spaces). As for integral preserving schemes the use of retractions will be essential, in particular efficient maps based on geodesics. For large dynamical systems on manifolds the methodology for reducing the dimension will follow ideas from shape analysis, collaboration with ESR4 is natural.