Abstract
In this article, we propose a Fourier pseudospectral method for solving the generalized improved Boussinesq equation. We prove the convergence of the semi-discrete scheme in the energy space. For various power nonlinearities, we consider three test problems concerning the propagation of a single solitary wave, the interaction of two solitary waves and a solution that blows up in finite time. We compare our numerical results with those given in the literature in terms of numerical accuracy. The numerical comparisons show that the Fourier pseudospectral method provides highly accurate results.
| Original language | English |
|---|---|
| Pages (from-to) | 995-1008 |
| Number of pages | 14 |
| Journal | Numerical Methods for Partial Differential Equations |
| Volume | 31 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 1 Jul 2015 |
Bibliographical note
Publisher Copyright:© 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 995-1008, 2015 © 2014 Wiley Periodicals, Inc.
Keywords
- blow-up
- collision of solitary waves
- convergence
- Fourier pseudospectral method
- semi-discrete scheme
- solitary waves
- the generalized improved Boussinesq equation