Lie-group methods

Arieh Iserles (1) , Hans Munthe-Kaas (2) , Syvert Nørsett (3) , Antonella Zanna (2)

1 DAMTP - Department of Applied Mathematics and Theoretical Physics
2 Department of Computer Science
3 Institute of Mathematics

Many differential equations of practical interest evolve on Lie groups or on manifolds acted upon by Lie groups. The retention of Lie-group structure under discretization is often vital in the recovery of qualitatively-correct geometry and dynamics and in the minimisation of numerical error. Having introduced requisite elements of differential geometry, this paper surveys the novel theory of numerical integrators that respect Lie-group structure, highlighting theory, algorithmic issues and a number of applications.

Domaines: Analyse numérique [math.NA]

Arieh Iserles, Hans Munthe-Kaas, Syvert Nørsett, Antonella Zanna. Lie-group methods. Acta Numerica, 2005, ⟨10.1017/S0962492900002154⟩. ⟨hal-01328729⟩