Splitting methods in the numerical integration of non-autonomous dynamical systems

We present a procedure leading to efficient splitting schemes for the time integration of explicitly time dependent partitioned linear differential equations arising when certain partial differential equations are previously discretized in space. In the first stage we analyze the order conditions of the corresponding autonomous problem and construct new 6th-order methods. In the second stage, by following a procedure previously designed by the authors, we generalize the methods to the time dependent case in such a way that no order reduction is present. The resulting schemes compare favorably with other integrators previously available.