An unconditionally stable difference scheme for the one-space-dimensional linear hyperbolic equation

An implicit three-level difference scheme of O(k(2) + h(2)) is discussed for the numerical solution of the linear hyperbolic equation u(tt) + 2alphau(t) + beta(2)u = u(xx) + f(x, t), alpha > beta greater than or equal to 0, in the region Omega = {(x, t) \ 0 < x < 1, t > 0} subject to appropriate initial and Dirichlet boundary conditions, where a and)3 are real numbers. We have used nine grid points with a single computational cell. The proposed scheme is unconditionally stable. The resulting system of algebraic equations is solved by using a tridiagonal solver. Numerical results demonstrate the required accuracy of the proposed scheme. (C) 2004 Elsevier Ltd. All rights reserved.