Gauss collocation methods for efficient structure preserving integration of post-Newtonian equations of motion

In this work, we present the hitherto most efficient and accurate method for the numerical integration of post-Newtonian equations of motion. We first transform the Poisson system as given by the post-Newtonian approximation to canonically symplectic form. Then we apply Gauss Runge-Kutta schemes to numerically integrate the resulting equations. This yields a convenient method for the structure preserving long-time integration of post-Newtonian equations of motion. In extensive numerical experiments, this approach turns out to be faster and more accurate (i) than previously proposed structure preserving splitting schemes and (ii) than standard explicit Runge-Kutta methods. We also show our approach to be appropriate for simulations on transitional precession.