A Time-Transformed Leapfrog Scheme

We present a time-transformed leapfrog scheme combined with the extrapolation method to construct an integrator for orbits in N-body systems with large mass ratios. The basic idea can be used to transform any second-order differential equation into a form which may allow more efficient numerical integration. When applied to gravitating few-body systems this formulation permits extremely close two-body encounters to be considered without significant loss of accuracy. The new scheme has been implemented in a direct N-body code for simulations of super-massive binaries in galactic nuclei. In this context relativistic effects may also be included.