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(k 2 +h 2 ) of Lees type for solving the three space dimensional linear hyperbolic equation u tt +2 f u t + g 2 u = u xx + u yy + 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 f >0 and g S 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.