The Chebyshev methods of Panovsky and Richardson as Runge-Kutta-Nystrِm methods

The two-step methods proposed by Panovsky and Richardson (this journal, 1988) and analysed by Coleman and Booth (this journal, 1992) are shown to be equivalent to certain Runge-Kutta-Nyström methods for differential equations of the form y″ = f(x,y). An important advantage of the new formulation is that it is no longer necessary to provide additional starting values at the beginning of a calculation or when the steplength or the order is changed; the new formulation is also more stable with respect to the propagation of rounding errors.