Explicit pseudo two-step Runge-Kutta methods for parallel computers

The aim of this paper is to investigate a class of explicit pseudo two-step Runge-Kutta methods of arbitrarily high order for nonstiff problems for sy stems of first-order differential equations. By using collocation technique s we can obtain for any given order of accuracy p, a stable pth-order expli cit pseudo two-step Runge-Kutta method requiring only one effective sequent ial right-hand side evaluation per step on multiprocessor computers. By a f ew widely-used test problems, we show the superiority of the methods consid ered in this paper over both sequential and parallel methods available in t he literature.