W. Auzinger, W. Herfort:
"Local error structures and order conditions in terms of Lie elements for exponential splitting schemes";
Opuscula Mathematica, 34 (2014), 2; S. 243 - 255.

Kurzfassung englisch:
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

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