An operator splitting technique for an unconditionally stable difference method for a linear three space dimensional hyperbolic equation with variable coefficients

We report a new three-step operator splitting method of O(k(2) + h(2)) for the difference solution of linear hyperbolic equation u(u) + 2alpha(x, y, z, t)u(t) + beta(2) (x, y, z, t)u = A (x, y, z, t)u(xx) + B(x, y, z, t)u(yy) + C(x, y, z, t)u(zz) + f(x, y, z, t) subject to appropriate initial and Dirichlet boundary conditions, where alpha(x, y, z, t) > beta (x, y, z, t) > 0 and A(x, y, z, t) > 0, B(x, y, z, t) > 0, C(x, y, z, t) > 0. The method is applicable to singular problems and stable for all choices of h > 0 and k > 0. The resulting system or algebraic equations is solved by using a tri-diagonal solver. Computational results are provided to demonstrate the viability of the new method. (C) 2004 Elsevier Inc. All rights reserved.