Hybrid symplectic integrators for planetary dynamics. Issue 4 (14th March 2019) - Rein, Hanno; Hernandez, David M; Tamayo, Daniel; Brown, Garett; Eckels, Emily; Holmes, Emma; Lau, Michelle; Leblanc, Réjean; Silburt, Ari
Abstract: Hybrid symplectic integrators such asMERCURY  are widely used to simulate complex dynamical phenomena in planetary dynamics that could otherwise not be investigated. A hybrid integrator achieves high accuracy during close encounters by using a high-order integration scheme for the duration of the encounter while otherwise using a standard second-order Wisdom–Holman scheme, thereby optimizing both speed and accuracy. In this paper we reassess the criteria for choosing the switching function that determines which parts of the Hamiltonian are integrated with the high-order integrator. We show that the original motivation for choosing a polynomial switching function inMERCURY is not correct. We explain the nevertheless excellent performance of theMERCURY integrator and then explore a wide range of different switching functions including an infinitely differentiable function and a Heaviside function. We find that using a Heaviside function leads to a significantly simpler scheme compared toMERCURY  , while maintaining the same accuracy in short-term simulations.