Setup of order conditions for splitting methods

Abstract

For operator splitting methods, an approach based on Taylor expansion and the particular structure of its leading term as an element of a free Lie algebra is used for the setup of a system of order conditions. Along with a brief review of the underlying theoretical background, we discuss the implementation of the resulting algorithm in computer algebra, in particular using Maple 18 (Maple is a trademark of MapleSoft™.). A parallel version of such a code is described, and its performance on a computational node with 16 threads is documented.