Through this paper, considering inhomogeneous broadening in amplification and pump bands, the dynamical behavior of an erbium-doped fiber amplifier (EDFA) is investigated. To this end, equations of propagation and populations are obtained with the erbium atoms being treated as three-level atoms. The governing equations comprise a set of PDEs of an infinite number which reduce to PDEs of the finite number using some mathematical tricks. The phenomena of spectral hole-burning and pump-mediated inhomogeneity are inspected by solving these equations through using the finite-difference (FD) method and calculating the gain difference spectrum.