Symplectic variable step size integration for N-body problems Original Research Article

Multiple time stepping can be applied to the leapfrog/Störmer/Verlet integrator so as to effect a variable step size algorithm. The strategy maintains the symplecticness, time-reversibility, and second-order accuracy of the leapfrog method. This method can be applied to 2-body central force interactions by partitioning them into distance classes and smoothly decomposing the potential energy into the sum of potential functions for the respective classes. The algorithm described here is much more efficient than leapfrog with very small step sizes and more accurate than leapfrog with larger step sizes.