  In this paper, a class of finite difference numerical techniques is presented
to solve the second-order linear inhomogeneous damped wave equation. The
consistency, stability, and convergences of these numerical schemes are
discussed. The results obtained are compared to the exact solution, ordinary
explicit, implicit finite difference methods, and the fourth-order compact
method (FOCM). The general idea of these methods is developed by using the
C0-semigroups operator theory. We also showed that the stability region for the
explicit finite difference scheme depends on the damping coefficient.
