  We present and numerically solve a modified form of the equation of motion
for a charged particle under the influence of an external force, taking into
account the radiation reaction. This covariant equation is integrodifferential,
as Dirac-R\"ohrlich's, but has several technical improvements. First, the
equation has the form of the second Newton law, with acceleration isolated on
the left hand side, and the force depending only on positions and velocities:
thus, the equation is linear in the highest derivative. Second, the total
four-force is by construction perpendicular to the four-velocity. And third, if
the external force vanishes for all future times, the total force and the
acceleration automatically vanish at present time. We show the advantages of
this equation by solving it numerically for several examples of external force.
