This paper focuses on the construction and analysis of explicit numerical methods of high dimensional stochastic nonlinear Schrodinger equations (SNLSEs). We first prove that the classical explicit numerical methods are unstable and suffer from the numerical divergence phenomenon. Then we propose a kind of explicit splitting numerical methods and prove that the structure-preserving splitting strategy is able to enhance the numerical stability. Furthermore, we establish the regularity analysis and strong convergence analysis of the proposed schemes for SNLSEs based on two key ingredients. One ingredient is proving new regularity estimates of SNLSEs by constructing a logarithmic auxiliary functional and exploiting the Bourgain space. Another one is providing a dedicated error decomposition formula and a novel truncated stochastic Gronwall's lemma, which relies on the tail estimates of underlying stochastic processes. In particular, our result answers the strong convergence problem of numerical methods for 2D SNLSEs emerged from [C. Chen, J. Hong and A. Prohl, Stoch. Partial Differ. Equ. Anal. Comput. 4 (2016), no. 2, 274-318] and [J. Cui and J. Hong, SIAM J. Numer. Anal. 56 (2018), no. 4, 2045-2069].

翻译：本文侧重于构建和分析高维随机非线性沙丁酸等式(SNLSES)的清晰数字方法。 我们首先证明古典的明显数字方法不稳定,并受到数字差异现象的影响。 然后我们提出一种明确的分割数字方法,并证明结构保护分解战略能够增强数字稳定性。 此外, 我们根据两个关键成分, 建立对SNLSE拟议办法的常规性分析和强烈趋同分析。 一个成分正在通过建立一个对数辅助功能和利用Bourgain空间来证明SNLSES的新的定期性估计。 另一个成分提供了一种专门的错误分解公式和新颖的断裂式Gronwallemma, 后者依赖于基本相切过程的尾数估计。 特别是, 我们的结果解决了2D SNLSese的拟议方法从[C. Chen, J. Hong和A. Prohl, Stoch. J. 部分 Diqur. Equ. 4, Eur. Anal. 2018, Nual. (2018, C. C. 274-AM. No.