%0 Journal Article
%F Auzinger2014
%A Auzinger, Winfried
%A Herfort, Wolfgang
%T Local error structures and order conditions in terms of Lie elements for exponential splitting schemes
%! Local error structures and order conditions in terms of Lie elements for exponential splitting schemes
%J Opuscula Mathematica
%O Opuscula Math.
%D 2014
%V 34
%N 2
%P 243-255
%R http://dx.doi.org/10.7494/OpMath.2014.34.2.243
%U http://dx.doi.org/10.7494/OpMath.2014.34.2.243
%X 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.
%K exponential splitting schemes
local error
defect
order conditions
free Lie algebra
%@ 1232-9274