Local error structures and order conditions in terms of Lie elements for exponential splitting schemes

Opuscula Mathematica

Winfried Auzinger¹  Wolfgang Herfort¹ 

[1] Vienna University of Technology, Institute for Analysis and Scientific Computing, Wiedner Hauptstrasse 8-10/E101, A-1040 Vienna, Austria;

关键词: exponential splitting schemes;    local error;    defect;    order conditions;    free Lie algebra;   

DOI  :  http://dx.doi.org/10.7494/OpMath.2014.34.2.243

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown