Explicit Parallel Two-Step Runge-Kutta-Nystroem Methods

摘要

The aim of this paper is to design a class of two-step Runge-Kutta-Nystrommethods of arbitrarily high order for the special second-order equation y(double prime)(t) = f(y(t)) for use on parallel computers. Starting with an s-stage implicit two-step Runge-Kutta-Nystrom method of order p with k = p/2 implicit stages, we apply the highly parallel predictor-corrector iteration process in P(EC)(sup m)E mode. In this way, we obtain an explicit two-step Runge-Kutta-Nystrom method that has order p for all m and that requires k(m+1) righthand side evaluations per step of which each k evaluation can be computed in parallel. By a number of numerical experiments, we show the superiority of the parallel predictor-corrector methods proposed in this paper over both sequential and parallel methods available in the literature.