2014/01/24 by Kelong Cheng, Cheng, Kelong, Wenqiang Feng +5 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Nonlinear Waves and Solitons #Differential Equations and Numerical Methods
paper · pdf · doi:10.48550/arxiv.1401.6327
In this paper, 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, an l_∞(0, T^*; H2) convergence for the solution and l_∞(0, T^*; l2) convergence for the time-derivative of the solution are obtained in this paper, instead of the l_∞(0, T^*; l2) convergence for the solution and the l_∞(0, T^*; H-2) convergence for the time-derivative, given in [17]. In addition, the stability and convergence of this method is shown to be unconditional for the time step in terms of the spatial grid size, compared with a severe restriction time step restriction Δt ≤ Ch2 reported in [17].