Authors: A. Zanna, H. Munthe-Kaas

Journal: Foundations of Computational Mathematics, Springer Verlag 1997.

Abstract: In the context of devising geometrical integrators that retain qualitative features of the underlying solution, we present a family of numerical methods (the method of iterated commutators, [5, 13]) to integrate ordinary differential equations that evolve on matrix Lie groups. The schemes apply to the problem of finding a numerical approximation to the solution of Y 0 = A(t;Y )Y; Y (0) = Y0 ; whereby the exact solution Y evolves in a matrix Lie group G and A is a matrix function on the associated Lie algebra g. We show that the method of iterated commutators, in a linear setting, is intrinsically related to Lie's reduction method for finding the fundamental solution of the Lie-group equation Y 0 = A(t)Y .

Hindsight notes: None yet.

1 Jan 1997