We consider various filtered time discretizations of the periodic Korteweg--de Vries equation: a filtered exponential integrator, a filtered Lie splitting scheme as well as a filtered resonance based discretisation and establish convergence error estimates at low regularity. Our analysis is based on discrete Bourgain spaces and allows to prove convergence in $L^2$ for rough data $u_{0} \in H^s,$ $s>0$ with an explicit convergence rate.
翻译:我们考虑了定期 Korteweg-de Vries 等式的各种过滤时间分解: 过滤的指数集成器、 过滤的谎言分解器以及基于过滤的共振分解法, 以及基于过滤的共振分解法, 并确定低常规度的趋同误差估计。 我们的分析基于离散的 Bourgain 空间, 并能够证明粗略数据 $u ⁇ 0}\ in H ⁇ s, $>0 美元, 并具有明确的趋同率 。