The aim of this paper is to consider parallel iteration schemes for a general class of pseudo twostep
Runge-Kutta-Nystr??m (RKN) methods of arbitrary high order for solving nonstiff initial-value
problems y??(t) = f(y(t)), y(t0) = y0, y? (t0) = y0 on parallel computers. Starting with an s-stage pseudo twostep
RKN method of order p* with w implicit stages, we apply the highly parallel PC iteration process in
P(EC)m E mode. The resulting PIPTRKN method (parallel-iterated pseudo two-step RKN method) uses an
optimal number of processors equal to w ?? p*/2. By a number of numerical experiments, we show the
superiority of the PIPTRKN methods proposed in this paper over both sequential and parallel methods
available in the literature.
