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The Magnus expansion and post-Lie algebras


Authors: Charles Curry, Kurusch Ebrahimi-Fard and Brynjulf Owren
Journal: Math. Comp. 89 (2020), 2785-2799
MSC (2010): Primary 34A26, 34G10, 65L05; Secondary 17B35
DOI: https://doi.org/10.1090/mcom/3541
Published electronically: May 26, 2020
MathSciNet review: 4136547
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Abstract: We relate the classical and post-Lie Magnus expansions. Intertwining algebraic and geometric arguments allows us to place the classical Magnus expansion in the context of Lie group integrators.


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Additional Information

Charles Curry
Affiliation: Department of Mathematical Sciences, Norwegian University of Science and Technology (NTNU), 7491 Trondheim, Norway
MR Author ID: 1076495
Email: charles.curry@ntnu.no

Kurusch Ebrahimi-Fard
Affiliation: Department of Mathematical Sciences, Norwegian University of Science and Technology (NTNU), 7491 Trondheim, Norway
MR Author ID: 672304
Email: kurusch.ebrahimi-fard@ntnu.no

Brynjulf Owren
Affiliation: Department of Mathematical Sciences, Norwegian University of Science and Technology (NTNU), 7491 Trondheim, Norway
MR Author ID: 292686
Email: brynjulf.owren@ntnu.no

Keywords: Magnus expansion, Lie group integration, pre-Lie algebra, post-Lie algebra
Received by editor(s): August 20, 2018
Received by editor(s) in revised form: July 12, 2019, and February 18, 2020
Published electronically: May 26, 2020
Additional Notes: This research was supported by The Research Council of Norway, the FRIPRO programme, grant No. 231632 and by the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska–Curie grant agreement No. 691070.
Article copyright: © Copyright 2020 American Mathematical Society