Context. Due to our increasing knowledge on the Galactic and stellar neighborhood of the Solar System, modern long-period comet motion studies have to take into account both stellar perturbations and the overall Galactic potential. Aims. Our aim is to propose algorithms and methods to perform numerical integration of a Solar System small body equations of motion much faster and at the same time with greater precision. Methods. We propose a new formulation of the equations of motion formulated in the Solar System barycentric frame but accurately accounting for the differential perturbations caused by the Galactic potential. To use these equations effectively we provide numerical ephemerides of the Galactic positions of the Sun and a set of potential stellar perturbers. Results. The proposed methods offer the precision higher by several orders of magnitude and simultaneously greatly reduce the necessary CPU time. The application of this approach is presented with the example of a detailed dynamical study of the past motion of comet C/2015 XY1.
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