@inproceedings{Kaas1995LieButcherTF,
title={Lie-Butcher theory for Runge-Kutta methods},
author={Hans Munthe Kaas},
year={1995}
}

Hans Munthe Kaas

Published 1995

Runge{Kutta methods are formulated via coordinate independent operations on manifolds. It is shown that there is an intimate connection between Lie series and Lie groups on one hand and Butcher's celebrated theory of order conditions on the other. In Butcher's theory the elementary di erentials are represented as trees. In the present formulation they appear as commutators between vector elds. This leads to a theory for the order conditions, which can be developed in a completely coordinateâ€¦Â CONTINUE READING