We discuss a new N -body simulation method for studying black hole binary dynamics .
This method avoids previous numerical problems due to large mass ratios and trapped orbits with short periods .
A treatment of relativistic effects is included when the associated time-scale becomes small .
Preliminary results with up to N = 2.4 \times 10 ^ { 5 } particles are obtained showing systematic eccentricity growth until the relativistic regime is reached , with subsequent coalescence in some cases .