Parallel predictor-corrector iteration of pseudo two-step RK methods for nonstiff IVPs

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 initial-value problems (IVPs) on parallel computers. Starting with ans-stage pseudo two-step RK method of orderp* withw 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 tow. 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.