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Time regularization of an Adams-Moulton-Cowell algorithm

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Abstract

This paper deals with the Adams-Moulton-Cowell multistep integrator, as described by Oestwinter and Cohen (1972). In order to evaluate the accuracy of the method, we started to test it in the case of the unperturbed two-body motion; numerical instability may arise by integrating first order systems. The accuracy is improved by applying a Sundmann transformation of the independent variable. The algorithm is then modified such that the equations of pure keplerian motion are integrated with respect to the new independent variable without truncation error; numerical experiments show the considerable improvement of accuracy and the reduction of computing time for Keplerian motion.

If terms of the disturbing function of the Earth are added to the central potential, the time-transformation is less effective. With a modification of this time-transformation as given by Moynot in 1971, it is possible to reduce the propagation of the truncation error in the J2 problem.

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Authors and Affiliations

  1. Groupe de Recherches de Géodésie Spatiale, Centre National d'Etudes Spatiales, 18 Avenue Edouard Belin, 31055, Toulouse Cedex 05, France

    N. Borderies

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  1. N. Borderies
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Borderies, N. Time regularization of an Adams-Moulton-Cowell algorithm. Celestial Mechanics 16, 291–308 (1977). https://doi.org/10.1007/BF01232656

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  • DOI: https://doi.org/10.1007/BF01232656

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