I need to integrate a system of coupled ODE in a manifold (SU(N)). I know that Runge-Kutta methods do not translate "automatically" to a integration scheme that preserves the manifold structure, but can be adapted (see, for example ).
The problem is that in adapting these RK methods the construction of embedded (i.g. adaptive size) integrators change. I have tried to look for references, but although it seems a straightforward problem, I found no reference.
Any ideas? Thanks!
 Hans Munthe-Kaas. "Runge-Kutta methods on Lie Groups".