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

摘要

We examine absolute stability of s-stage explicit Runge-Kutta-Nyström (R-K-N) methods of order s for s=2, 3, 4 for y″=ƒ(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.