Symplectic propagators for the Kepler problem with time-dependent mass

[EN] New numerical integrators specifically designed for solving the two-body gravitational problem with a time-varying mass are presented. They can be seen as a generalization of commutator-free quasi-Magnus exponential integrators and are based on the compositions of symplectic flows. As a consequence, in their implementation they use the mapping that solves the autonomous problem with averaged masses at intermediate stages. Methods up to order eight are constructed and shown to be more efficient than other symplectic schemes on numerical examples. This work has been funded by Ministerio de Economia, Industria y Competitividad (Spain) through project MTM2016-77660-P (AEI/FEDER, UE). Kopylov has also been partly supported by Grant GRISOLIA/2015/A/137 from the Generalitat Valenciana. Bader, P.; Blanes Zamora, S.; Casas, F.; Kopylov, N. (2019). Symplectic propagators for the Kepler problem with time-dependent mass. Celestial Mechanics and Dynamical Astronomy. 131(6):1-19. https://doi.org/10.1007/s10569-019-9903-7 Abraham, R., Marsden, J.: Foundations of Mechanics, 2nd edn. Addison-Wesley, Reading (1978) Adams, F., Anderson, K., Bloch, A.: Evolution of planetary systems with time-dependent stellar mass-loss. Month. Not. R. Astronom. Soc. 432, 438–454 (2013) Alvermann, A., Fehske, H.: High-order commutator-free exponential time-propagation of driven quantum systems. J. Comput. Phys. 230, 5930–5956 (2011) Arnold, V.: Mathematical Methods of Classical Mechanics, 2nd edn. Springer, Berlin (1989) Blanes, S.: Time-average on the numerical integration of non-autonomous differential equations. SIAM J. Numer. Anal. 56, 2513–2536 (2018) Blanes, S., Casas, F.: A Concise Introduction to Geometric Numerical Integration. CRC Press, Boca Raton (2016) Blanes, S., Casas, F., Ros, J.: Processing symplectic methods for near-integrable Hamiltonian systems. Celest. Mech. Dyn. Astron. 77, 17–35 (2000) Blanes, S., Casas, F., Oteo, J., Ros, J.: The Magnus expansion and some of its applications. Phys. Rep. 470, 151–238 (2009) Blanes, S., Casas, F., Thalhammer, M.: High-order commutator-free quasi-Magnus exponential integrators for non-autonomous linear evolution equations. Comput. Phys. Commun. 220, 243–262 (2017) Blanes, S., Casas, F., Thalhammer, M.: Convergence analysis of high-order commutator-free quasi Magnus exponential integrators for nonautonomous linear evolution equations of parabolic type. IMA J. Numer. Anal. 38, 743–778 (2018) Danby, J.: Fundamentals of Celestial Mechan