Unconditionally stable ADI scheme of higher-order for linear hyperbolic equations
Author:
- 30 June 2010
- journal article
- research article
- Published by Taylor & Francis in International Journal of Computer Mathematics
- Vol. 87 (13) , 3030-3038
Abstract
An unconditionally stable alternating direction implicit (ADI) method of higher-order in space is proposed for solving two- and three-dimensional linear hyperbolic equations. The method is fourth-order in space and second-order in time. The solution procedure consists of a multiple use of one-dimensional matrix solver which produces a computational cost effective solver. Numerical experiments are conducted to compare the new scheme with the existing scheme based on second-order spatial discretization. The effectiveness of the new scheme is exhibited from the numerical results.Keywords
This publication has 9 references indexed in Scilit:
- New unconditionally stable difference schemes for the solution of multi-dimensional telegraphic equationsInternational Journal of Computer Mathematics, 2009
- A high-order compact ADI method for solving three-dimensional unsteady convection-diffusion problemsNumerical Methods for Partial Differential Equations, 2005
- An operator splitting technique for an unconditionally stable difference method for a linear three space dimensional hyperbolic equation with variable coefficientsApplied Mathematics and Computation, 2005
- High order ADI method for solving unsteady convection–diffusion problemsJournal of Computational Physics, 2004
- An operator splitting method for an unconditionally stable difference scheme for a linear hyperbolic equation with variable coefficients in two space dimensionsApplied Mathematics and Computation, 2004
- An Unconditionally Stable ADI Method for the Linear Hyperbolic Equation in Three Space DimensionsInternational Journal of Computer Mathematics, 2002
- High order difference schemes for the system of two space second order nonlinear hyperbolic equations with variable coefficientsJournal of Computational and Applied Mathematics, 1996
- A Classification of Split Difference Methods for Hyperbolic Equations in Several Space DimensionsSIAM Journal on Numerical Analysis, 1969
- Alternating Direction Methods for Hyperbolic Differential EquationsJournal of the Society for Industrial and Applied Mathematics, 1962