Symplectic propagators for the Kepler problem with time-dependent mass

Abstract

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.