Behaviour of a new type of Runge–Kutta methods when integrating satellite orbits

Recently, González, Martín and Farto have developed new numerical methods (RKGM methods) of Runge–Kutta type and fixed step size for the numerical integration of perturbed oscillators. Moreover, it seems natural to study the behaviour of these new methods for the accurate integration of orbital problems after the application of linearizing transformation, such us KS or BF due to the fact that in these variables, the structure of the problem is of the form of perturbed oscillators, for which the methods constructed are indicated. In this paper, we check the efficiency of these new methods when integrating the satellite problem. The RKGM methods show a very good behaviour when they compete with other, classical and special, methods. This revised version was published online in July 2006 with corrections to the Cover Date.