We investigate a filtered Lie-Trotter splitting scheme for the ``good" Boussinesq equation and derive an error estimate for initial data with very low regularity. Through the use of discrete Bourgain spaces, our analysis extends to initial data in $H^{s}$ for $0<s\leq 2$, overcoming the constraint of $s>1/2$ imposed by the bilinear estimate in smooth Sobolev spaces. We establish convergence rates of order $\tau^{s/2}$ in $L^2$ for such levels of regularity. Our analytical findings are supported by numerical experiments.

翻译：我们研究了一种针对"好"布西内斯克方程的滤波Lie-Trotter分裂格式，并推导了极低正则性初始数据的误差估计。通过使用离散Bourgain空间，我们的分析将初始数据扩展到$H^{s}$（$0<s\leq 2$），克服了光滑Sobolev空间中双线性估计施加的$s>1/2$约束。我们建立了此类正则性水平下$L^2$中$\tau^{s/2}$阶的收敛速率。我们的分析结果得到了数值实验的支持。