Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4967931 | Journal of Computational Physics | 2017 | 24 Pages |
Abstract
A Fourier pseudo-spectral method that conserves mass and energy is developed for a two-dimensional nonlinear Schrödinger equation. By establishing the equivalence between the semi-norm in the Fourier pseudo-spectral method and that in the finite difference method, we are able to extend the result in Ref. [56] to prove that the optimal rate of convergence of the new method is in the order of O(Nâr+Ï2) in the discrete L2 norm without any restrictions on the grid ratio, where N is the number of modes used in the spectral method and Ï is the time step size. A fast solver is then applied to the discrete nonlinear equation system to speed up the numerical computation for the high order method. Numerical examples are presented to show the efficiency and accuracy of the new method.
Related Topics
Physical Sciences and Engineering
Computer Science
Computer Science Applications
Authors
Yuezheng Gong, Qi Wang, Yushun Wang, Jiaxiang Cai,