An exponential integrator sine pseudospectral method for the generalized improved Boussinesq equation

Su C., Muslu G. M.

BIT NUMERICAL MATHEMATICS, vol.61, no.4, pp.1397-1419, 2021 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 61 Issue: 4
  • Publication Date: 2021
  • Doi Number: 10.1007/s10543-021-00865-0
  • Title of Journal : BIT NUMERICAL MATHEMATICS
  • Page Numbers: pp.1397-1419
  • Keywords: Error estimate, Exponential integrator, Improved Boussinesq equation, Long-time dynamics, Sine pseudospectral method

Abstract

A Deuflhard-type exponential integrator sine pseudospectral (DEI-SP) method is proposed and analyzed for solving the generalized improved Boussinesq (GIBq) equation. The numerical scheme is based on a second-order exponential integrator for time integration and a sine pseudospectral discretization in space. Rigorous analysis and abundant experiments show that the method converges quadratically and spectrally in time and space, respectively. Finally the DEI-SP method is applied to investigate the complicated and interesting long-time dynamics of the GIBq equation.