A Fourier pseudospectral method for the “good” Boussinesq equation with second‐order temporal accuracy
Abstract
In this article, we discuss the nonlinear stability and convergence of a fully discrete Fourier pseudospectral method coupled with a specially designed second‐order time‐stepping for the numerical solution of the “good” Boussinesq equation. Our analysis improves the existing results presented in earlier literature in two ways. First, a convergence for the solution and convergence for the time‐derivative of the solution are obtained in this article, instead of the convergence for the solution and the convergence for the time‐derivative, given in De Frutos, et al., Math Comput 57 (1991), 109–122. In addition, we prove that this method is unconditionally stable and convergent for the time step in terms of the spatial grid size, compared with a severe restriction time step restriction required by the proof in De Frutos, et al., Math Comput 57 (1991), 109–122.© 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 202–224, 2015
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jun 24, 2014
- Source ID
- 10.1002/num.21899
Entities
People
- Cheng Wang
- Kelong Cheng
- Sigal Gottlieb
- Wenqiang Feng
Organizations
- Air Force Office of Scientific Research
- National Science Foundation
- Southwest University of Science and Technology
- University of Massachusetts
- University of Tennessee