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.
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).