Charles Curry

Charles Curry, Kurusch Ebrahimi-Fard, Hans Munthe-Kaas

We explain the notion of a post-Lie algebra and outline its role in the theory of Lie group integrators.

Charles Curry, Brynjulf Owren

We introduce variable stepsize commutator free Lie group integrators, where the error control is achieved using embedded Runge-Kutta pairs.

Charles Curry, Alexander Schmeding

We relate two notions of local error for integration schemes on Riemannian homogeneous spaces, and show how to derive global error estimates from such local bounds. In doing so, we prove for the first time that the Lie-Butcher theory of Lie group integrators leads to global error estimates.