A MULTIPLE TIME-STEP SYMPLECTIC ALGORITHM FOR INTEGRATING CLOSE ENCOUNTERS

We present a new symplectic algorithm that has the desirable propertie s 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 time step technique. When the bodies are well separated, the algorithm has the speed of MVS methods, and whenever tw o bodies suffer a mutual encounter, the time step for the relevant bod ies is recursively subdivided to whatever level is required. We demons trate the power of this method using several tests of the technique. W e believe that this algorithm will be a valuable tool for the study of planetesimal dynamics and planet formation.