Unconditionally stable difference schemes for a one-space-dimensional linear hyperbolic equation

A few explicit difference schemes are discussed for the numerical solution of the linear hyperbolic equation utt + 2α ut + β2u = uxx + f(x, t), α > 0, β > 0, in the region Ω = {(x, t)∣a < x < b, t > 0} subject to appropriate initial and Dirichlet boundary conditions, where α and β are real numbers. The proposed scheme is showed to be unconditionally stable, and numerical result is presented.