Scattering and uniform in time error estimates for splitting method in NLS

Rémi Carles Chunmei Su

Analysis of PDEs mathscidoc:2205.03006

2021.10
We consider the nonlinear Schr{ö}dinger equation with a defocusing nonlinearity which is mass-(super)critical and energy-subcritical. We prove uniform in time error estimates for the Lie-Trotter time splitting discretization. This uniformity in time is obtained thanks to a vectorfield which provides time decay estimates for the exact and numerical solutions. This vectorfield is classical in scattering theory, and requires several technical modifications compared to previous error estimates for splitting methods.
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@inproceedings{rémi2021scattering,
  title={Scattering and uniform in time error estimates for splitting method in NLS},
  author={Rémi Carles, and Chunmei Su},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220519160351419716286},
  year={2021},
}
Rémi Carles, and Chunmei Su. Scattering and uniform in time error estimates for splitting method in NLS. 2021. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220519160351419716286.
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