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Local error structures and order conditions in terms of Lie elements for exponential splitting schemes

Auzinger W., Herfort W.

Opuscula Mathematica

2014

Vol. 34, no. 2

243--256

We discuss the structure of the local error of exponential operator splitting methods. In particular, it is shown that the leading error term is a Lie element, i.e., a linear combination of higher-degree commutators of the given operators. This structural assertion can be used to formulate a simple algorithm for the automatic generation of a minimal set of polynomial equations representing the order conditions, for the general case as well as in symmetric settings.