We consider the nonlinear Schr{\"o}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.

翻译：我们考虑的是非线性Schr}o}丁格尔方程式,它具有一个非线性非线性,即质量(超级)临界值和能量亚临界值。我们证明,对利特罗特时间分离的时间误差估算是统一的。这种时间一致性的实现要归功于一个矢量字段,它提供了精确和数字解决方案的时间衰变估算值。这个矢量字段在散射理论中是典型的,它需要与先前的分裂方法误估值相比进行若干技术修改。