Splitting methods for non-autonomous separable dynamical systems

A large number splitting methods for autonomous separable systems exists in the literature which have been designed for many different structures of the vector field. However, the performance of most of these methods is diminished and their orders of accuracy are frequently reduced when applied to non-autonomous problems. Based on the formal solution obtained from the Magnus series expansion, we show how to modify a standard splitting method for autonomous problems to treat non-autonomus systems with similar or better efficiency. We illustrate this technique to build new fourth and sixth order schemes whose performance is then illustrated on several numerical examples.