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

作者：Cheng Kelong; Feng Wenqiang; Gottlieb Sigal; Wang Cheng^*

来源：Numerical Methods for Partial Differential Equations, 2015, 31(1): 202-224.

DOI：10.1002/num.21899

• aliasing error
• fully discrete Fourier pseudospectral method
• good Boussinesq equation
• stability and convergence

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.

• 出版日期2015-1
• 单位西南科技大学