Splitting and composition methods for explicit time dependence in separable dynamical systems

We consider splitting methods for the numerical integration of non-autonomous sep- arable differential equations. Splitting methods have been extensively used as geometric numerical integrators during the last years showing excellent performances (both qualitatively and quantita- tively) when applied on many problems. They are designed for autonomous separable systems and a substantial number of methods tailored for different structures of the equations have recently ap- peared. When these methods are used on non-autonomous problems, usually their performance diminishes considerably, and even they can lose the order of accuracy. Previous attempts to preserve such performance on non-autonomous problems required to modify, in a non-trivial way, the existing methods. In this paper, we present a simple alternative which, in many relevant cases, allows to retain the high performance of the splitting methods using the same schemes as for the autonomous problems. This technique is applied on different problems and its performance is illustrated on several numerical examples.