A Deuflhard-type exponential integrator Fourier pseudospectral method for the "Good" Boussinesq equation

TL;DR

This paper introduces an explicit, efficient Fourier pseudospectral method using a Deuflhard-type exponential integrator for solving the

Contribution

It develops a fully explicit spectral scheme for the GB equation with quadratic temporal convergence and spectral spatial accuracy, without CFL constraints.

Findings

Quadratic convergence in time.

Spectral accuracy in space.

Confirmed effectiveness through numerical experiments.

Abstract

We propose an exponential integrator Fourier pseudospectral method DEI-FP for solving the "Good" Boussinesq (GB) equation. The numerical scheme is based on a Deuflhard-type exponential integrator and a Fourier pseudospectral method for temporal and spatial discretizations, respectively. The scheme is fully explicit and efficient due to the fast Fourier transform. Rigorous error estimates are established for the method without any CFL-type condition constraint. In more details, the method converges quadratically and spectrally in time and space, respectively. Extensive numerical experiments are reported to confirm the theoretical analysis and to demonstrate rich dynamics of the GB equation.