A Fourier Pseudospectral Method for the "Good" Boussinesq Equation with Second-Order Temporal Accuracy

In this article, we discuss the nonlinear stability and convergence of a fully discrete Fourier pseudospectral method coupled with a specially designed second-order time-stepping for the numerical solution of the " good" Boussinesq equation. Our analysis improves the existing results presented in earlier literature in two ways. First, l(infinity)(0, T *; H-2) convergence for the solution and l(infinity) (0, T*; l(2)) convergence for the timederivative of the solution are obtained in this article, instead of the l(infinity)(0, T*; l(2)) convergence for the solution and the l(infinity)(0, T*; H-2) convergence for the time-derivative, given in De Frutos, et al., Math Comput 57 (1991), 109-122. In addition, we prove that this method is unconditionally stable and convergent for the time step in terms of the spatial grid size, compared with a severe restriction time step restriction Delta t <= Ch(2) required by the proof in De Frutos, et al., Math Comput 57 (1991), 109-122. (C) 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 202-224, 2015