A linearly-implicit and conservative Fourier pseudo-spectral method for the 3D Gross-Pitaevskii equation with angular momentum rotation

In this paper, a linearly-implicit Fourier pseudo-spectral method which preserves discrete mass and energy is developed for the time-dependent 3D Gross-Pitaevskii equation with additional angular momentum rotation. By establishing several discrete semi-norm equivalences between the Fourier pseudo-spectral method and the finite difference method, we establish an optimal H-1-error estimate for the proposed scheme without any restrictions on the grid ratio. The convergent rate of the numerical solution is proved to be of order O(N-r + tau(2)), where N is the number of spatial nodes and tau is the time step. Numerical results are reported to verify the efficiency and accuracy of our new method. (C) 2020 Elsevier B.V. All rights reserved.