A new class of numerical integration methods for differential equations on manifolds is presented. Canonical coordinates of the second kind is used for representing the Lie group locally be means of its corresponding Lie algebra. The methods involve computation of the coordinate map and the inverse of its differential. We consider in depth how to choose a basis for the Lie algebra so that evaluation of these operations is computationally inexpensive. Numerical experiments illustrating the theory are presented.

References:

[1] B. Owren and A. Marthinsen: Integration methods based on canonical coordinates of the second kind, preprint Numerics No. 5/1999, Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim, Norway

MINISIMPOSIUM SESSION: 12. Lie Group methods