Norges Teknisk-naturvitenskapelige Universitet Quadrature Methods Based on the Cayley Transform Quadrature Methods Based on the Cayley Transform

Integration of Lie type equations on matrix Lie groups using Magnus series methods has recently been proposed by Iserles and N rsett. The methods use the exponential mapping, whose computation may be very costly. In this paper a smaller class of Lie groups is considered, for which the exponential mapping can be replaced by e.g. the Cayley transform or the diagonal Pad e approximants. Particular methods are being derived, and numerical experiments that illustrate and verify properties of the new methods are included. AMS Subject Classi cation: 65L06, 34A50