Unconditionally stable ADI scheme of higher-order for linear hyperbolic equations

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:

• hyperbolic equation
• high-order difference scheme
• ADI method
• unconditional stability

2000 AMS Subject Classification:

• 65M06

Acknowledgements

This research was supported by Sultan Qaboos University under Grant IG/SCI/DOMAS/07/08.