This paper is devoted to variable stepsize strategy implementations of a class of explicit pseudo
two-step Runge-Kutta-Nystr??m methods of arbitrarily high order for solving nonstiff problems for systems
of special second-order differential equations. The constant stepsize explicit pseudo two-step Runge-Kutta-
Nystr??m methods are developed into variable stepsize ones and equipped with embedded formulas giving a
cheap error estimate for stepsize control. By two examples of widely-used test problems, a pseudo two-step
Runge-Kutta-Nystr??m method of order 8 implemented with variable stepsize strategy is shown to be much
more efficient than parallel and sequential codes available in the literature. With stringent error tolerances,
this new explicit pseudo two-step Runge-Kutta-Nystr??m method is even superior to sequential codes in a
sequential computer. ?? 2001 IMACS.
