An unconditionally stable alternating direction implicit scheme for the two space dimensional linear hyperbolic equation

We report a new unconditionally stable implicit alternating direction implicit (ADI) scheme of O(k(2) + h(2)) for the difference solution of linear hyperbolic equation u(tt) + 2 alphau(t) + beta (2)u = u(xx) + u(yy) + f(x, y, t), alpha > beta greater than or equal to 0, 0 < x, y < 1, t > 0 subject to appropriate initial and Dirichlet boundary conditions, where alpha > 0 and beta : 0 are real numbers. The resulting system of algebraic equations is solved by split method. Numerical results are provided to demonstrate the efficiency and accuracy of the method. (C) 2001 John Wiley & Sons, Inc.