In Huang and Leimkuhler [SIAM J. Sci. Comput. 18 (1997) 239–256], a variable step-size, semi-explicit variant of the explicit Störmer–Verlet method has been suggested for the time-reversible integration of Newtonʹs equations of motion. Here we propose a f

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 recent work in this area. Next, building on earlier work of Iserles and Nørsett, we prove that an appropriate truncation of the expansion is time symmetric. Moreover, we develop a 6th-order Lie-group solver based on the Magnus expansion which requires just three function evaluations and the calculation of seven commutators. The paper is accompanied by a number of numerical experiments.