A Deuflhard-type exponential integrator Fourier pseudo-spectral method for the ``good'' Boussinesq equation (Q2307424)

This paper propose a Deuflhard-type exponential integrator Fourier pseudo-spectral (DEI-FP) method for solving the ``Good'' Boussinesq (GB) equation. The numerical scheme is based on a Deuflhard-type exponential integrator and a Fourier pseudo-spectral method for temporal and spatial discretizations, respectively. The method converges quadratically and spectrally in time and space, respectively. An unconditional convergence is proved in a genneral energy norm: the \(H^{m}\) norm in \(z\) combined with the \(H^{m-2}\) norm in \(z_{t}\) for \(m>1/2\). At last, the author presents extensive numerical experiments reveal rich and complicated dynamical phenomena for the GB equation, such as elastic interaction, blow-up phenomena, recovering as a static soliton and so forth.