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

Abstract

A few explicit difference schemes are discussed for the numerical solution of the linear hyperbolic equation u tt + 2 α u t + β 2 u = u xx + 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.