Abstract
This paper investigates a class of explicit pseudo three-step Runge-Kutta methods for arbitrarily high order nonstiff initial value problems for systems of first-order differential equations. By using collocation techniques and by suitably choosing collocation points we can obtain a stable \(s\)-stage explicit pseudo three-step Runge-Kutta method (EPThRK method) of order \(p=2s\) requiring only one effective sequential f-evaluation per step on \(s\)-processor parallel computers. By a few widely-used test problems, we show the superiority of the new EPThRK methods proposed in this paper over red well-known parallel PIRK codes and efficient sequential ODEX, DOPRI5 and DOP853 codes available in the literature.
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