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.