Abstract
The aim of this paper is to consider parallel iteration schemes for a general class of pseudo two-step Runge-Kutta-Nyström (RKN) methods of arbitrary high order for solving nonstiff initial-value problems y″( t) = f(y( t)), y( t 0) = y 0, y′( t 0) = y 0 on parallel computers. Starting with an s-stage pseudo two-step 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.
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