Behaviour of the SMF method for the numerical integration of satellite orbits

The SMF algorithms were recently developed by the authors as a multistep generalization of the Scheifele G-functions one-step method. Like the last, the proposed codes integrate harmonic oscillations without truncation error and the perturbing parameter appears as a factor of that error when integrating perturbed oscillations. Therefore they seemed to be convenient for the accurate integration of orbital problems after the application of linearizing transformations, such as KS or BE In this paper we present several numerical experiments concerning the propagation of Earth satellite orbits, that illustrate the performance of the the SMF method. In general, it provides greater accuracy than the usual standard algorithms for similar computational cost.