An unconditionally stable ADI method for the linear hyperbolic equation in three space dimensions

Abstract

An unconditionally stable alternating direction implicit (ADI) method of O(k2+h2) of Lees type for solving the three space dimensional linear hyperbolic equation utt+2αu tβ2u = uxx+ uyy+u zz+f(x, y, z, t), 0 < x, y, z < 1, t > 0 subject to appropriate initial and Dirichlet boundary conditions is proposed, where α > 0 and β ≥ 0 are real numbers. For this method, we use a single computational cell. The resulting system of algebraic equations is solved by three step split method. The new method is demonstrated by a suitable numerical example. © 2002 Taylor & Francis Ltd.