2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/193879We calculate the self-force acting on a particle with scalar charge moving on a generic geodesic around a Schwarzschild black hole. This calculation requires an accurate computation of the retarded scalar field produced by the moving charge; this is done numerically with the help of a fourth-order convergent finite-difference scheme formulated in the time domain. The calculation also requires a regularization procedure, because the retarded field is singular on the particle's world line; this is handled mode-by-mode via the mode-sum regularization scheme first introduced by Barack and Ori. This paper presents the numerical method, various numerical tests, and a sample of results for mildly eccentric orbits as well as ``zoom-whirl'' orbits.18 pages, 18 figures, RevTeX4 some typos fixed, published versionGeneral Relativity and Quantum Cosmologytext