An operator splitting method for an unconditionally stable difference scheme for a linear hyperbolic equation with variable coefficients in two space dimensions

A new three level implicit unconditionally stable operator splitting method of O(k(2) + h(2)) is proposed for the numerical solution of two space dimensional linear hyperbolic equation u(u)+ 2alpha(xj,t)u(t) + beta(2)(x,y,t)u = A(x,y,t)u(xx) + B(x,j,t)u(yy) +f(x,v,t), 0 < x, y < 1, t > 0 subject to appropriate initial and Dirichlet boundary conditions, where alpha(x,y,t) > beta(x,y,t) > 0, A(x, y, t) > O B(x,y,t) > 0. The resulting system of algebraic equations is solved by two-step split method. The proposed method is applicable to the problems having singularity at x = 0. Numerical results are provided to demonstrate the utility of the new method. (C) 2003 Elsevier Inc. All rights reserved.