A second order accuracy in time, Fourier pseudo-spectral numerical scheme for "Good" Boussinesq equation

Zeyu Xia, ,School of Mathematical Sciences University of Electronic Science and Technology of China Chengdu, Sichuan 611731, China, Xiaofeng Yang, ,Department of Mathematics, University of South Carolina Columbia, SC 29208
2017 Discrete and continuous dynamical systems. Series B  
The nonlinear stability and convergence of a numerical scheme for the "Good" Boussinesq equation is provided in this article, with second order temporal accuracy and Fourier pseudo-spectral approximation in space. Instead of introducing an intermediate variable ψ to approximate the first order temporal derivative, we apply a direct approximation to the second order temporal derivative, which in turn leads to a reduction of the intermediate numerical variable and improvement in computational
more » ... n computational efficiency. A careful analysis reveals an unconditional stability and convergence for such a temporal discretization. In addition, by making use of the techniques of aliasing error control, we obtain an ∞ (0, T * ; H 2 ) convergence for u and ∞ (0, T * ; 2 ) convergence for the discrete time-derivative of the solution in this paper, in comparison with the ∞ (0, T * ; 2 ) convergence for u and the ∞ (0, T * ; H −2 ) convergence for the time-derivative, given in [19] .
doi:10.3934/dcdsb.2020089 fatcat:mykvyzld55ga7ea2e42isuwhni