Abstract: Turkel studied a hyperbolic equation using composite method. Motivated by Turkel, we study a corresponding problem (wave propagation problem) using a numerical scheme, namely, central difference scheme. The stability and convergence of the scheme are investigated. From the analysis the order of dissipativity for the central difference scheme is four compared to that of the composite scheme, which is six; hence, the central difference scheme is less dissipative than the composite scheme. Another feature of the central difference scheme is that it allows more refinement of the grid size than the composite scheme and this refinement helps to improve the accuracy of the central difference scheme. A numerical example based on a wave propagation problem (initial boundary value problem) is solved using analytic and computer methods and the results are compared with that of the central difference scheme.