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Computer simulations in QCD are based on the discretization of the theory ona Euclidean lattice. To compute the mean value of an observable, usually theHybrid Monte Carlo method is applied. Here equations of motion, derived from anHamiltonian, have to be solved numerically. Commonly the Leapfrog(Stoermer-Verlet) method or splitting methods with multiple timescales \`a laSexton-Weingarten are used to integrate the dynamical system, defined on a Liegroup. Here we formulate time-reversible higher order integrators based onimplicit partitioned Runge-Kutta schemes and show that they allow for largerstep-sizes than the Leapfrog method. Since these methods are based on aninfinite series of exponential functions, we concentrate on the truncation ofthis series with respect to the global error and accuracy. Finally, we see thatthe global error of a SPRK scheme is always even such that a convergence orderof one is gained for methods with odd convergence order.

Accuracy of Symmetric Partitioned Runge-Kutta Methods for Differential Equations on Lie-Groups