  We numerically calculate the dissipative part of the self-force on a scalar
charge moving on a circular, geodesic, equatorial orbit in Kerr spacetime. The
solution to the scalar field equation is computed by separating variables and
is expressed as a mode sum over radial and angular modes. The force is then
computed in two ways: a direct, instantaneous force calculation which uses the
half-retarded-minus-half-advanced field, and an indirect method which uses the
energy and angular momentum flux at the horizon and at infinity to infer the
force. We are able to show numerically and analytically that the force-per-mode
is the same for both methods. To enforce the boundary conditions (ingoing
radiation at the horizon and outgoing radiation at infinity for the retarded
solution) numerical solutions to the radial equation are matched to asymptotic
expansions for the fields at the boundaries. Recursion relations for the
coefficients in the asymptotic expansions are given in an appendix.
