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W. Auzinger, W. Herfort:
"Local error structures and order conditions in terms of Lie elements for exponential splitting schemes";
in: "ASC Report 23/2013", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2013, ISBN: 978-3-902627-06-3, 1 - 15.

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.

Exponential splitting schemes, local error, defect, order conditions, free Lie algebra

http://www.asc.tuwien.ac.at/preprint/2013/asc23x2013.pdf