Numerical integration methods for the double-bracket flow

In this paper new methods up to order four based on the Magnus expansion are proposed for the numerical integration of the double-bracket equation. The Magnus series is constructed term-by-term by means of recurrences and a bound on the convergence domain is also provided. The new integrators preserve the most salient qualitative features of the flow and are computationally more efficient than other standard Lie-group solvers, such as the Runge–Kutta–Munthe-Kaas class of algorithms.