Abstract
Runge-Kutta-Nystrom (RKN) codes for the solution of the initial value problem for the general second order differential system have been developed recently, although the methodology on which they are based was known many years ago. In this paper we try to examine the efficiency of several known general Runge-Kutta-Nystrom (GRKN) methods by posing some criteria of cost and accuracy. These methods supplied with the corresponding interpolants, have been applied to some problems of Celestial Dynamics. The results obtained show that these codes have a good response in the approximation of the solution of these problems.
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Tsitouras, C., Papageorgiou, G. & Kalvouridis, T. On the efficiency of Runge-Kutta-Nystrom methods with interpolants for solving equations of the form Y″ = F(T, Y, Y′) over short timespans. Celestial Mech Dyn Astr 53, 329–346 (1992). https://doi.org/10.1007/BF00051815
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DOI: https://doi.org/10.1007/BF00051815