  In this paper the performance of a parallel iterated Runge-Kutta method is
compared versus those of the serial fouth order Runge-Kutta and Dormand-Prince
methods. It was found that, typically, the runtime for the parallel method is
comparable to that of the serial versions, thought it uses considerably more
computational resources. A new algorithm is proposed where full parallelization
is used to estimate the best stepsize for integration. It is shown that this
new method outperforms the others, notably, in the integration of very large
systems.
