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(tau(4) + h(4)) for the difference solution of a two-dimensional second-order non-homogeneous linear hyperbolic equation u(tt) + 2 alpha u(t) + beta(2)u = u(xx) + u(yy) + f (x, y, t), 0 < x, y < 1, t > 0, where alpha > beta >= 0. Stability analysis of the method has been carried out. Finally, numerical examples are used to illustrate the efficiency of the new difference scheme. (C) 2009 Elsevier B.V. All rights reserved.