Explicit pseudo two-step runge-kutta methods for parallel computers^∗

^∗This work was partly supported by DAAD, N.R.P.F.S. and QG-96-02

Abstract

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 systems of first-order differential equations. By using collocation techniques we can obtain for any given order of accuracy p, a stable pth-order explicit pseudo two-step Runge-Kutta method requiring only one effective sequential right-hand side evaluation per step on multiprocessor computers. By a few widely-used test problems, we show the superiority of the methods considered in this paper over both sequential and parallel methods available in the literature.

Keywords:

• Runge-Kutta methods
• Two-Step Runge-Kutta methods
• stability
• parallelism

C.R. Category:

• G.1.6

^∗This work was partly supported by DAAD, N.R.P.F.S. and QG-96-02

^∗This work was partly supported by DAAD, N.R.P.F.S. and QG-96-02

Notes

^∗This work was partly supported by DAAD, N.R.P.F.S. and QG-96-02