A new fourth-order compact finite difference scheme for the two-dimensional second-order hyperbolic equation

In this paper, we propose a three level compact difference scheme of O(τ4+h4)O(τ4+h4) for the difference solution of a two-dimensional second-order non-homogeneous linear hyperbolic equation utt+2αut+β2u=uxx+uyy+f(x,y,t),00, where α>β≥0α>β≥0. Stability analysis of the method has been carried out. Finally, numerical examples are used to illustrate the efficiency of the new difference scheme.