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

• Published in: Applied mathematics letters Vol. 17; no. 1; pp. 101 - 105
• Main Author: Mohanty, R.K.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 2004; Elsevier
• Subjects: Damped wave equation; Exact sciences and technology; Implicit scheme; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Pade approximation; Partial differential equations, initial value problems and time-dependant initial-boundary value problems; RMS errors; Sciences and techniques of general use; Second-order linear hyperbolic equation; Telegraph equation; Unconditionally stable; Unconditionally stable; Pade approximation; Telegraph equation; Second-order linear hyperbolic equation; Damped wave equation; RMS errors; Implicit scheme; Wave equation; Second order equation; Difference scheme; Stability; Implicit method; RMS error; Partial differential equation; Numerical analysis; Linear equation; Numerical solution; Hyperbolic equation; Algebraic equation; Damped equation; Padé approximation
• ISSN: 0893-9659; 1873-5452
• DOI: 10.1016/S0893-9659(04)90019-5

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.