Splitting Methods for Non-autonomous Hamiltonian Equations

We present an algorithm for numerically integrating non-autonomous Hamiltonian differential equations. Special attention is paid to the separable case and, in particular, a new fourth-order splitting method is presented which in a certain measure is optimal. In combination with a new way of handling non-autonomous problems, the schemes we present are based on Magnus expansions and they show very promising results when applied to Hamiltonian ODEs and PDEs.