In this paper, we study two kinds of structure-preserving splitting methods, including the Lie--Trotter type splitting method and the finite difference type method, for the stochasticlogarithmic Schr\"odinger equation (SlogS equation) via a regularized energy approximation. We first introduce a regularized SlogS equation with a small parameter $0<\epsilon\ll1$ which approximates the SlogS equation and avoids the singularity near zero density. Then we present a priori estimates, the regularized entropy and energy, and the stochastic symplectic structure of the proposed numerical methods. Furthermore, we derive both the strong convergence rates and the convergence rates of the regularized entropy and energy. To the best of our knowledge, this is the first result concerning the construction and analysis of numerical methods for stochastic Schr\"odinger equations with logarithmic nonlinearities.

翻译：在本文中,我们研究了两种结构保护分解方法,包括利托式分解法和有限的差异类型法,即通过正常的能源近似值的沙沙质阵列方程式(SlogS 等方程式)。我们首先采用了一种常规的SlogS等式,其参数小,为0. ⁇ epsilon\ll1美元,接近SlogS等式,避免接近零密度的奇异性。然后我们提出了一个先验估计,固定的酶和能量,以及拟议数字方法的随机共振结构。此外,我们从中推算出已正规化的英式和能量的强趋同率和趋同率。据我们所知,这是关于构建和分析具有对数非线性的Schr\“量方程式”的数值方法的第一个结果。