New methods for large dynamical range problems in planetary formation
  Modern N-body techniques for planetary dynamics are generally based on symplectic algorithms specially adapted to the Kepler problem. These methods have proven very useful in studying planet formation, but typically require the timestep for all objects to be set to a small fraction of the orbital period of the innermost body. This computational expense can be prohibitive for even moderate particle number for many physically interesting scenarios, such as recent models of the formation of hot exoplanets, in which the semimajor axis of possible progenitors can vary by orders of magnitude. We present new methods which retain most of the benefits of the standard symplectic integrators but allow for radial zones with distinct timesteps. These approaches should make simulations of planetary accretion with large dynamical range tractable. As proof of concept we present preliminary science results from an implementation of the algorithm as applied to an oligarchic migration scenario for forming hot Neptunes. 
D.S. McNeil and R.P. Nelson