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.
Comment: arXiv admin note: text overlap with arXiv:0908.3757, arXiv:0908.3760