Application of a fourth-order compact ADI method to solve a two-dimensional linear hyperbolic equation

Abstract

In this paper, a compact alternating direction implicit method is developed for solving a linear hyperbolic equation with constant coefficients. Its stability criterion is determined by using von Neumann method. It is shown through a discrete energy method that this method can attain fourth-order accuracy in both time and space with respect to H ¹- and L ²-norms provided the stability condition is fulfilled. Its solvability is also analysed in detail. Numerical results confirm the convergence orders and efficiency of our algorithm.

Keywords:

• hyperbolic equation
• compact finite difference scheme
• ADI method
• stability
• convergence
• solvability

2010 AMS Subject Classifications:

• 65M06
• 65M12
• 65M15

Acknowledgements

Authors are deeply grateful to three anonymous referees, editor and Principal Editor Prof. Abdul Khaliq for their insightful comments and helpful suggestions, which have greatly improved this article. This work is supported by NSFC (Nos. 11171125, 91130003), NSFH (No. 2011CDB289) and SRF of NHU (No. Ec200907255).