Can the post-Newtonian gravitational waveform of an inspiraling binary be improved by solving the energy balance equation numerically? art. no. 104015

The detection of gravitational waves from inspiraling compact binaries usin g matched filtering depends crucially on the availability of accurate templ ate waveforms. We determine whether the accuracy of the templates' phasing can be improved by solving the post-Newtonian energy balance equation numer ically, rather than las is normally done) analytically within the post-Newt onian perturbative expansion. By specializing to the limit of a small mass ratio, we find evidence that there is no gain in accuracy.