In a previous paper, based on the black hole perturbation approach, we formulated a new analytical method for regularizing the self-force acting on a particle of small mass $mu$ orbiting a Schwarzschild black hole of mass $M$, where $mull M$. In our method, we divide the self-force into the $tilde S$-part and $tilde R$-part. All the singular behaviors are contained in the $tilde S$-part, and hence the $tilde R$-part is guaranteed to be regular. In this paper, focusing on the case of a scalar-charged particle for simplicity, we investigate the precision of both the regularized $tilde S$-part and the $tilde R$-part required for the construction of sufficiently accurate waveforms for almost circular inspiral orbits. For the regularized $tilde S$-part, we calculate it for circular orbits to 18 post-Newtonian (PN) order and investigate the convergence of the post-Newtonian expansion. We also study the convergence of the remaining $tilde{R}$-part in the spherical harmonic expansion. We find that a sufficiently accurate Green function can be obtained by keeping the terms up to $ell=13$.
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