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 ( τ 4 + h 4 ) for the difference solution of a two-dimensional second-order non-homogeneous linear hyperbolic equation u t t + 2 α u t + β 2 u = u x x + u y y + f ( x , y , t ) , 0 < x , y < 1 , t > 0 , where α > 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.