TY  - JOUR
ID  - Auzinger2014
LB  - Auzinger2014
AU  - Auzinger, Winfried
AU  - Herfort, Wolfgang
TI  - Local error structures and order conditions in terms of Lie elements for exponential splitting schemes
ST  - Local error structures and order conditions in terms of Lie elements for exponential splitting schemes
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2014
VL  - 34
IS  - 2
SP  - 243
EP  - 255
DO  - http://dx.doi.org/10.7494/OpMath.2014.34.2.243
UR  - http://dx.doi.org/10.7494/OpMath.2014.34.2.243
AB  - 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.
KW  - exponential splitting schemes
KW  - local error
KW  - defect
KW  - order conditions
KW  - free Lie algebra
SN  - 1232-9274
ER  -