A conservative Fourier pseudo-spectral method for the nonlinear Schrodinger equation

作者：Gong, Yuezheng; Wang, Qi; Wang, Yushun^*; Cai, Jiaxiang

来源：Journal of Computational Physics, 2017, 328: 354-370.

DOI：10.1016/j.jcp.2016.10.022

• Nonlinear Schrodinger equation
• Fourier pseudo-spectral method
• Unconditional convergence
• FFT

A Fourier pseudo-spectral method that conserves mass and energy is developed for a two-dimensional nonlinear Schrodinger 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(N-r + tau(2)) in the discrete L-2 norm without any restrictions on the grid ratio, where N is the number of modes used in the spectral method and tau 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.

• 出版日期2017-1-1
• 单位南京师范大学; 南开大学; 淮阴师范学院; 北京计算科学研究中心