A Multiple Time Step Symplectic Algorithm for Integrating Close Encounters

We present a new symplectic algorithm that has the desirable properties of the sophisticated but highly efficient numerical algorithms known as Mixed Variable Symplectic (MVS) methods, and that in addition can handle close encounters between objects. This technique is based on a variant of the standard MVS methods, but it handles close encounters by employing a multiple timestep technique. When the bodies are well separated, the algorithm has the speed of MVS methods, and whenever two bodies suffer a mutual encounter, the timestep for the relevant bodies is recursively subdivided to whatever level is required. We demonstrate the power of this method using several tests of the technique. We believe that this algorithm will be a valuable tool for the study of planetesimal dynamics and planet formation. Subject headings: celestial mechanics, stellar dynamics --- methods: numerical --- planetary systems --- solar system: general 1 Present address: Department of Physics, University of Cali...