Runge-Kutta methods on Lie groups

We construct generalized Runge-Kutta methods for integration of differential equations evolving on a Lie group. The methods are using intrinsic operations on the group, and we are hence guaranteed that the numerical solution will evolve on the correct manifold. Our methods must satisfy two different criteria to achieve a given order.• CoefficientsAi,j andbj must satisfy the classical order conditions. This is done by picking the coefficients of any classical RK scheme of the given order.• We must construct functions to correct for certain non-commutative effects to the given order.