Abstract 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 + τ 2 ) , where N is the number of spatial nodes and τ is the time step. Numerical results are reported to verify the efficiency and accuracy of our new method.

中文翻译：

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具有角动量旋转的 3D Gross-Pitaevskii 方程的线性隐式和保守傅立叶伪谱方法

摘要 在本文中，针对具有附加角动量旋转的瞬态 3D Gross-Pitaevskii 方程，开发了一种保持离散质量和能量的线性隐式傅立叶伪谱方法。通过在傅立叶伪谱法和有限差分法之间建立几个离散的半范数等价，我们为所提出的方案建立了一个最优的H 1 -误差估计，对网格比没有任何限制。证明数值解的收敛速度为 O ( N − r + τ 2 ) 阶，其中 N 是空间节点的数量，τ 是时间步长。报告了数值结果以验证我们新方法的效率和准确性。