  In this paper, a complete Lie symmetry analysis of the damped wave equation
with time-dependent coefficients is investigated. Then the invariant solutions
and the exact solutions generated from the symmetries are presented. Moreover,
a Lie algebraic classifications and the optimal system are discussed. Finally,
using Chebyshev pseudo-spectral method (CPSM), a numerical analysis to solve
the invariant solutions corresponded the Lie symmetries of main equation is
presented. This method applies the Chebyshev-Gauss-Lobatto points as
collocation points.
