# Numerical integration on manifolds

Hi all,

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 [1]).

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!

[1] Hans Munthe-Kaas. "Runge-Kutta methods on Lie Groups".

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My impression is that Iserles and his coauthors have worked extensively on this - have you tried looking up his papers? –  Yemon Choi Feb 16 '12 at 16:46
You also might want to check out this article: Unitary integrators and applications to continuous orthonormalization techniques by Dieci, Russell, and van Vleck. –  Paul Tupper Feb 17 '12 at 5:34