A new unconditionally stable ADI compact scheme for the two-space-dimensional linear hyperbolic equation

We formulate a new alternating direction implicit compact scheme of O(T-2+h(4)) for the linear hyperbolic equation u(tt)+2 alpha u(t)+beta(2)u=u(xx)+u(yy)+f(x, y, t), 00 and beta >= 0 are real numbers. In this article, we show the method is unconditionally stable by the Von Neumann method. At last, numerical demonstrations are given to illustrate our result.