The subject of this paper is the investigation of the Magnus expansion of a solution of the linear differential equation y′=a(t)y, y(0)∈G, where G is a Lie group and View the MathML source being the Lie algebra of G. We commence with a brief survey of rec

Integration of Lie type equations on matrix Lie groups using Magnus series methods has recently been proposed by Iserles and Nørsett. 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 Padé approximants. Particular methods are derived, and numerical experiments that illustrate and verify properties of the new methods are included.