An introduction to Lie group integrators -- basics, new developments and applications
Elena Celledoni, H{\aa}kon Marthinsen, Brynjulf Owren
TL;DR
This paper provides an accessible overview of Lie group integrators, discusses various applications, and introduces new symplectic integrators and generalized discrete gradient methods on Lie groups.
Contribution
It offers a foundational introduction, explores applications, and presents novel symplectic integrators and generalized discrete gradient methods for Lie groups.
Findings
Introduction to Lie group methods
Application examples of Lie group integrators
New symplectic integrators on cotangent bundles of Lie groups
Abstract
We give a short and elementary introduction to Lie group methods. A selection of applications of Lie group integrators are discussed. Finally, a family of symplectic integrators on cotangent bundles of Lie groups is presented and the notion of discrete gradient methods is generalised to Lie groups.
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