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

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(u)+2alphau(t)+beta(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 alpha > 0 and beta greater than or equal to 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.