Absolute stability of explicit Runge-Kutta-Nyström methods for y″=ƒ(x,y, y′)

We examine absolute stability of s-stage explicit Runge-Kutta-Nyström (R-K-N) methods of order s for $\text{s=2, 3, 4}\text{for}\text{y″=?(x, y, y′)}$ by applying these methods to the test equation: y″+2λy′+λ²y=0, λ>0. We show the existence of R-K-N methods of orders two, three and four possessing intervals of absolute stability as large as that of explicit Runge-Kutta (r-K) methods of respective orders.