A Fourier Pseudospectral Method for a Generalized Improved Boussinesq Equation

作者：Borluk Handan; Muslu Gulcin M^*

来源：Numerical Methods for Partial Differential Equations, 2015, 31(4): 995-1008.

DOI：10.1002/num.21928

• the generalized improved Boussinesq equation
• Fourier pseudospectral method
• semi-discrete scheme
• convergence
• solitary waves
• collision of solitary waves
• blow-up

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.

• 出版日期2015-7