Opuscula Math. 34, no. 2 (2014), 243-255
http://dx.doi.org/10.7494/OpMath.2014.34.2.243
Opuscula Mathematica
Local error structures and order conditions in terms of Lie elements for exponential splitting schemes
Winfried Auzinger
Wolfgang Herfort
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.
Mathematics Subject Classification: 17B08, 17B80, 65J08, 65M15, 68W30.
- Winfried Auzinger
- Vienna University of Technology, Institute for Analysis and Scientific Computing, Wiedner Hauptstrasse 8-10/E101, A-1040 Vienna, Austria
- Wolfgang Herfort
- Vienna University of Technology, Institute for Analysis and Scientific Computing, Wiedner Hauptstrasse 8-10/E101, A-1040 Vienna, Austria
- Received: 2013-09-04.
- Revised: 2014-03-03.
- Accepted: 2014-03-03.
