Iterated Runge-Kutta methods on distributed memory multiprocessors

In this article, we consider the iterated Runge-Kutta (IRK) method which is an iteration method based on a predictor-corrector scheme for the solution of ordinary differential equations. The method uses embedded formulae to control the stepsize. We present different algorithms of the IRK method on distributed memory multiprocessors using appropriate communication primitives. The theoretical performance analysis and a runtime simulation allow us to value the presented algorithms. An implementation on the Intel iPSC/860 confirms the predicted runtimes