We consider the nonlinear Schrödinger 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.

中文翻译：

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NLS 分裂法时间误差估计的分散性和均匀性

我们考虑具有质量（超）临界和能量亚临界的散焦非线性的非线性薛定谔方程。我们证明了 Lie-Trotter 时间分裂离散化的时间误差估计是统一的。由于向量场提供了精确解和数值解的时间衰减估计，因此获得了时间上的均匀性。这个矢量场在散射理论中是经典的，与以前的分裂方法的误差估计相比需要进行一些技术修改。