The method of iterated commutators for ordinary differential equations on Lie groups

We construct numerical methods to integrate ordinary di erential equations that evolve on Lie groups. These schemes are based on exponentials and iterated commutators, they are explicit and their order analysis is relatively simple. Thus we can construct group-invariant integrators of arbitrarily high order. Among other applications we show that this approach can be used to obtain new symplectic schemes when applied to Hamiltonian problems. Some numerical experiments are presented.

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