In this paper, we propose a linearly implicit Fourier pseudo-spectral scheme, which preserves the total mass and energy conservation laws for the damped nonlinear Schrödinger equation in three dimensions. With the aid of the semi-norm equivalence between the Fourier pseudo-spectral method and the finite difference method, an optimal L²-error estimate for the proposed method without any restriction on the grid ratio is established by analyzing the real and imaginary parts of the error function. Numerical results are addressed to confirm our theoretical analysis.

中文翻译：

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三维阻尼非线性Schrödinger方程的线性保持线性隐式傅里叶拟谱方案

在本文中，我们提出了一种线性隐式傅里叶伪谱方案，该方案在三个维度上保留了阻尼非线性Schrödinger方程的总质量守恒律和能量守恒律。借助于傅立叶伪谱方法和有限差分方法之间的半范等价，通过分析网格的实部和虚部，建立了该方法的最优L ²误差估计，而对网格比率没有任何限制。错误功能。数值结果表明我们的理论分析。