  We consider a discrete nonlinear Klein-Gordon equations with damping and
external drive. Using a small amplitude ansatz, one usually approximates the
equation using a damped, driven discrete nonlinear Schr\"odinger equation.
Here, we show for the first time the justification of this approximation by
finding the error bound using energy estimate. Additionally, we prove the local
and global existence of the Schr\"odinger equation. Numerical simulations are
performed that describe the analytical results. Comparisons between discrete
breathers of the Klein-Gordon equation and discrete solitons of the discrete
nonlinear Schr\"odinger equation are presented.
