This paper investigates parallel predictor-corrector (PC) iteration schemes based on direct
collocation Runge-Kutta-Nystr??m (RKN) corrector methods with continuous output formulas for solving
nonstiff initial-value problems (IVPs) for systems of special second-order differential equations y?? (t) = f (t,
y (t)). Consequently, the resulting parallel-iterated RKN-type PC methods are provided with continuous
output formulas. The continuous numerical approximations are also used for predicting the stage values in
the PC iteration processes. In this way, we obtain parallel PC methods with continuous output formulas and
high-order predictors. Applications of the resulting parallel PC methods to a few widely-used test problems
reveal that these new parallel PC methods are much more efficient when compared with the parallel-iterated
RKN (PIRKN) methods and the sequential ODEX2 and DOPRIN codes from the literature. ?? 2006
IMACS.
