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

Abstract

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 + 2 αu t + β 2 u = u xx + f( x, t), α > β ≥ 0, in the region Ω = {(x,t) ∥ 0 < x < 1, t > 0} subject to appropriate initial and Dirichlet boundary conditions, where α 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.