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

An implicit three-level difference scheme of O(k2 + h2) is discussed for the numerical solution of the linear hyperbolic equation utt + 2αut + β2u = uxx + f(x, t), a > β > 0, in the region Ω = {(x,t) | 0 < x < 1, t > 0} subject to appropriate initial and Dirichlet boundary conditions, where a and β 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.