A second order operator splitting numerical scheme for the "good" Boussinesq equation

The nonlinear stability and convergence analyses are presented for a second order operator splitting scheme applied to the "good" Boussinesq equation, coupled with the Fourier pseudo-spectral approximation in space. Due to the wave equation nature of the model, we have to rewrite it as a system of two equations, for the original variable u and v = u(t), respectively. In turn, the second order operator splitting method could be efficiently designed. A careful Taylor expansion indicates the second order truncation error of such a splitting approximation, and a linearized stability analysis for the numerical error function yields the desired convergence estimate in the energy norm. In more details, the convergence in the energy norm leads to an l(infinity) (0, T*; H-2) convergence for the numerical solution u and l(infinity) (0, T*; l(2)) convergence for v = u(t). And also, the presented convergence is unconditional for the time step in terms of the spatial grid size, in comparison with a severe time step restriction, Delta t <= Ch(2), required in many existing works. (C) 2017 IMACS. Published by Elsevier B.V. All rights reserved.