This paper discusses predictor-corrector iteration schemes (PC iteration schemes) based on direct
collocation-based Runge-Kutta-Nystr??m corrector methods (RKN corrector methods) for solving nonstiff
initial-value problems (IVPs) for systems of special second-order differential equations y??(t)=f(y(t)). Our
approach is to regard the well-known parallel-iterated RKN methods (PIRKN methods) as PC iteration
processes in which the simple, low-order last step value predictors are replaced with the high-order Adamstype
predictors. Moreover, the parameters of the new direct collocation-based RKN corrector methods are
chosen in such a way that the convergence rate of the considered PC iteration processes is optimized. In this
way, we obtain parallel PC methods with fast convergence and high-accurate predictions. Application of the
resulting parallel PC methods to a few widely-used test problems reveals that the sequential costs are very
much reduced when compared with the parallel and sequential explicit RKN methods from the literature. ??
2001 OPA (Overseas Publishers Association) N.V. Published by license under the Gordon and Breach
Science Publishers imprint.
