  In this work, we present two numerical methods to approximate solutions of
systems of dissipative sine-Gordon equations that arise in the study of
one-dimensional, semi-infinite arrays of Josephson junctions coupled through
superconducting wires. Also, we present schemes for the total energy of such
systems in association with the finite-difference schemes used to approximate
the solutions. The proposed methods are conditionally stable techniques that
yield consistent approximations not only in the domains of the solution and the
total energy, but also in the approximation to the rate of change of energy
with respect to time. The methods are employed in the estimation of the
threshold at which nonlinear supratransmission takes place, in the presence of
parameters such as internal and external damping, generalized mass, and
generalized Josephson current. Our results are qualitatively in agreement with
the corresponding problem in mechanical chains of coupled oscillators, under
the presence of the same parameters.
