  In this paper, we present a new hybrid algorithm for the time integration of
collisional N-body systems. In this algorithm, gravitational force between two
particles is divided into short-range and long-range terms, using a
distance-dependent cutoff function. The long-range interaction is calculated
using the tree algorithm and integrated with the constant-timestep leapfrog
integrator. The short-range term is calculated directly and integrated with the
high-order Hermite scheme. We can reduce the calculation cost per orbital
period from O(N^2) to O(N log N), without significantly increasing the
long-term integration error. The results of our test simulations show that
close encounters are integrated accurately. Long-term errors of the total
energy shows random-walk behaviour, because it is dominated by the error caused
by tree approximation.
