@Article{Auzinger2014,
author = "Auzinger, Winfried and Herfort, Wolfgang",
title = "Local error structures and order conditions in terms of Lie elements for exponential splitting schemes",
journal = "Opuscula Math.",
year = "2014",
volume = "34",
number = "2",
pages = "243--255",
doi = "http://dx.doi.org/10.7494/OpMath.2014.34.2.243",
url = "http://dx.doi.org/10.7494/OpMath.2014.34.2.243",
abstract = "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.",
keywords = "exponential splitting schemes, local error, defect, order conditions, free Lie algebra",
issn = "1232-9274"
}