Journal of Applied Mathematics
Volume 2013 (2013), Article ID 267106, 11 pages
Research Article

High Efficient Numerical Methods for Viscous and Nonviscous Wave Problems

1Center for Combinatorics, Nankai University, Tianjin 300071, China
2Institute of Plasma Physics, Chinese Academy of Sciences, Hefei, Anhui Province 230031, China
3School of Mathematical Sciences, Tianjin Normal University, Tianjin 300387, China

Received 9 October 2012; Revised 31 March 2013; Accepted 22 April 2013

Academic Editor: Jae-Wook Kim

Copyright © 2013 Xiujie Lv et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper is concerned with accurate and efficient numerical methods for solving viscous and nonviscous wave problems. The paper first introduces a new second-order PR-ADI like scheme. For an efficient simulation, the scheme is also extended to a high-order compact PRADI like method. Both of them have the advantages of unconditional stability, less impact of the perturbing terms on the accuracy, and being convenient to compute the boundary values of the intermediates. Besides this, the compact scheme has high-order accuracy and costs less in computational time. Numerical results are presented to show the accuracy and efficiency of the new algorithms.