Setup of Order Conditions for Splitting Methods

This article is based on earlier papers where an approach based on Taylor expansion and the structure of its leading term as an element of a free Lie algebra was described for the setup of a system of order conditions for operator splitting methods. Along with a brief review of these materials and some theoretical background, we discuss the implementation of the ideas from these papers in computer algebra, in particular using Maple 18. A parallel version of such a code is described.