Parallel Predictor-Corrector Iteration of Pseudo Two- Step RK Methods for Nonstiff IVPs

Abstract

A parallel predictor-corrector (PC) iteration scheme for a general class of pseudo two-step Runge- Kutta methods (PTRK methods) of arbitrarily high order is analyzed for solving first-order nonstiff initialvalue problems (IVPs) on parallel computers. Starting with an s-stage pseudo two-step RK method of order p* with w implicit stages, we apply the highly parallel PC iteration process in P(EC)mE mode. The resulting parallel-iterated pseudo two-step RK method (PIPTRK method) uses an optimal number of processors equal to w. By a number of numerical experiments, we show the superiority of the PIPTRK methods proposed in this paper over both sequential and parallel methods available in the literature.