A general class of explicit pseudo two-step RKN methods on parallel computers

The aim of this paper is to investigate a general class of explicit pseudo two-step Runge-Kutta-Nystrom methods (RKN methods) of arbitrarily high orde r for nonstiff problems for systems of special second-order differential eq uations y "(t) = f(y(t)). Order and stability considerations show that we c an obtain for any given p, a stable p(th)-order explicit pseudo two-step RK N method requiring p - 2 right-hand side evaluations per step of which each evaluation can be obtained in parallel. Consequently, on a multiprocessor computer, only one sequential right-hand side evaluation per step is requir ed. By a few widely-used test problems, we show the superiority of the meth ods considered in this paper over both sequential and parallel methods avai lable in the literature. (C) 1999 Elsevier Science Ltd. All rights reserved .