  Synge's problem consists in to determine the dynamics of two point electrical
charges interacting through their electromagnetic fields, without to take into
account the radiation terms due to the self-forces in each charge. We discuss
how this problem is related to the question on to establish initial conditions
for the electromagnetic fields that are compatible with the two point charges
system isolation, that is, the charges are free from the action of external
forces. This problem stems from the existence of inter-temporal constraints for
the charges trajectories, which implies that the relativistic Newton equations
for the charges is not a system of ODEs, but rather a system of Functional
Differential Equations (FDEs). We developed a new method to obtain global
solutions that satisfies this system of FDEs and a given initial condition for
the charges positions and velocities. This method allows the construction of a
recursive numerical algorithm that only use integration methods for ODEs
systems. Finally, we apply this algorithm to obtain numerical approximations
for the quasi-circular solutions that are predicted in Synge's problem.
