Filtered Lie-Trotter splitting for the "good" Boussinesq equation: low regularity error estimates
<|reference_start|>Filtered Lie-Trotter splitting for the "good" Boussinesq equation: low regularity error estimates: 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.<|reference_end|>
@article{ji2024filtered,
    title={Filtered Lie-Trotter splitting for the "good" Boussinesq equation: low
  regularity error estimates},
    author={Lun Ji, Hang Li, Alexander Ostermann, Chunmei Su},
    journal={arXiv preprint arXiv:2402.11266},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.11266},
    primaryClass={math.NA cs.NA}
}