  In recent work we presented an explicit and non-perturbative derivation of
the classical radiation reaction force for a cut-off modelled by a special
choice of tubes of finite radius around the charge trajectories. In this paper,
we provide a further, simpler and so-called reduced radiation reaction model
together with a systematic numerical comparison between both the respective
radiation reaction forces and the Landau-Lifschitz force as a reference. We
explicitly construct the numerical flow for the new forces and present the
numerical integrator used in the simulations, a Gauss-Legendre method adapted
for delay equations. For the comparison, we consider the cases of a constant
electric field, a constant magnetic field, and a plane wave. In all these
cases, the deviations between the three force laws are shown to be small. This
excellent agreement is an argument for plausibility of both new equations but
also means that an experimental differentiation remains hard. Furthermore, we
discuss the effect of the tube radius on the trajectories, which turns out to
be small in the regarded regimes. We conclude with a comparison of the
numerical cost of the corresponding integrators and find that the integrator of
the reduced radiation reaction to be numerically most and the integrator of
Landau-Lifschitz least efficient.
