Why Magnus expansion

Abstract

A short story about the origins of Magnus Expansion, why we got involved and how it led us to meet Geometric Integration. We present a biographical draft of Wilhelm Magnus, a sketchy discussion of what is the expansion which carries his name and a derivation of the formalism equations. We explain the important feature that makes the expansion an appropriate tool to develop Geometric Integration schemes.

Keywords:

• Magnus expansion
• geometric integration
• Dyson expansion
• Magnus operator
• exponential perturbation theory

2010 Mathematics Subject Classification:

• 34C60

Acknowledgments

The authors thank an anonymous referee for the very constructive comments.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Biographical details with no specific reference are taken from one of the following sources: (https://mathshistory.st-andrews.ac.uk/Biographies/Magnus/, https://de.wikipedia.org/wiki/HansHeinrichWilhelmMagnus) and some personal recollections of Magnus in [3].

Additional information

Funding

The work of J.A.O. has been partially supported by the Spanish MINECO [grant number PID2019-109592GB-100].