  We develop two numerical methods to solve the differential equations with
deviating arguments for the motion of two charges in the action-at-a-distance
electrodynamics. Our first method uses St\"urmer's extrapolation formula and
assumes that a step of integration can be taken as a step of light ladder,
which limits its use to shallow energies. The second method is an improvement
of pre-existing iterative schemes, designed for stronger convergence and can be
used at high-energies.
