  We present a comparison of different numerical techniques for the integration
of variational equations. The methods presented can be applied to any
autonomous Hamiltonian system whose kinetic energy is quadratic in the
generalized momenta, and whose potential is a function of the generalized
positions. We apply the various techniques to the well-known H\'enon-Heiles
system, and use the Smaller Alignment Index (SALI) method of chaos detection to
evaluate the percentage of its chaotic orbits. The accuracy and the speed of
the integration schemes in evaluating this percentage are used to investigate
the numerical efficiency of the various techniques.
