The filtered Lie splitting scheme is an established method for the numerical integration of the periodic nonlinear Schr\"{o}dinger equation at low regularity. Its temporal convergence was recently analyzed in a framework of discrete Bourgain spaces in one and two space dimensions for initial data in $H^s$ with $0<s\leq 2$. Here, this analysis is extended to dimensions $d=3, 4, 5$ for data satisfying $d/2-1 < s \leq 2$. In this setting, convergence of order $s/2$ in $L^2$ is proven. Numerical examples illustrate these convergence results.

翻译：滤波李分裂格式是用于低正则性条件下周期非线性薛定谔方程数值积分的一种成熟方法。近期，该格式的时间收敛性在离散Bourgain空间框架下得到分析，针对一维和二维空间中具有$H^s$正则性（$0<s\leq 2$）的初值问题。本文将此分析推广至维度$d=3,4,5$，针对满足$d/2-1 < s \leq 2$的初值数据。在此设定下，证明了$L^2$范数下$s/2$阶的收敛性。数值算例验证了这些收敛结果。