Publications in Scientific Journals:
W. Auzinger, W. Herfort:
"Local error structures and order conditions in terms of Lie elements for exponential splitting schemes";
Opuscula Mathematica,
34
(2014),
2;
243
- 255.
English 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
"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)
http://dx.doi.org/10.7494/OpMath.2014.34.2.243
Electronic version of the publication:
http://publik.tuwien.ac.at/files/PubDat_227555.pdf
Created from the Publication Database of the Vienna University of Technology.