  The accuracy of time-domain solutions of the inhomogeneous Teukolsky equation
is improved significantly. Comparing energy fluxes in gravitational waves with
highly accurate frequency-domain results for circular equatorial orbits in
Schwarzschild and Kerr, we find agreement to within 1% or better, which we
believe can be even further improved. We apply our method to orbits for which
frequency-domain calculations have a relative disadvantage, specifically
high-eccentricity (elliptical and parabolic) "zoom-whirl" orbits, and find the
energy fluxes, waveforms, and characteristic strain in gravitational waves.
