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.

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Cite this article as:
Winfried Auzinger, Wolfgang Herfort, Local error structures and order conditions in terms of Lie elements for exponential splitting schemes, Opuscula Math. 34, no. 2 (2014), 243-255, http://dx.doi.org/10.7494/OpMath.2014.34.2.243

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