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In this paper, a complete Lie symmetry analysis of the damped wave equationwith time-dependent coefficients is investigated. Then the invariant solutionsand 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 solvethe invariant solutions corresponded the Lie symmetries of main equation ispresented. This method applies the Chebyshev-Gauss-Lobatto points ascollocation points.

Lie Symmetry Classification and Numerical Analysis of KdV Equation with Power-law Nonlinearity