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

Abstract

We formulate a new alternating direction implicit compact scheme of O(τ2+h 4) for the linear hyperbolic equation u tt +2α u t +β2 u=u xx +u yy +f(x, y, t), 0<x, y<1, 0<t≤T, subject to appropriate initial and Dirichlet boundary conditions, where α>0 and β≥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.