In this paper, a general and detailed study of linear stability of Runge-Kutta-Nyström (RKN) methods is given. In the case that arbitrarily stiff problems are integrated, we establish a condition that RKN methods must satisfy so that a uniform bound for stability can be achieved. This condition is not satisfied by any method in the literature. Therefore, a stable method is constructed and some numerical comparisons are made. © 2005 Elsevier B.V. All rights reserved.
Alonso-Mallo, I., Cano, B., & Moreta, M. J. (2006). Stability of Runge-Kutta-Nyström methods. In Journal of Computational and Applied Mathematics (Vol. 189, pp. 120–131). https://doi.org/10.1016/j.cam.2005.01.005