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

Rémi Carles (1) , Chunmei Su (2, 3)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 Yau Mathematical Science Center and Beijing Institute of Mathematical Sciences and Applications
3 THU - Tsinghua University [Beijing]

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.

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Rémi Carles, Chunmei Su. Scattering and uniform in time error estimates for splitting method in NLS. Foundations of Computational Mathematics, In press, ⟨10.1007/s10208-022-09600-9⟩. ⟨hal-03403443v2⟩