Error estimates for a fully discrete spectral scheme for nonlinear Boussinesq systems.

A high-order fully discrete numerical scheme is developed for the solution of the initial-periodic boundary value problem for a nonlinear family of Boussinesq systems by combining a Fourier collocation spectral approximation in space and the classical fourth-order Runge-Kutta scheme for the time discretization. The error bounds have spectral accuracy in space and optimal order in time. Numerical experiments are shown to validate the accuracy of method and the convergence rate. Furthermore, the solitary waves and their interactions are studied numerically.