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

2021/10/27 by Carles, Rémi, Su, Chunmei · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2110.14258

Abstract

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.

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• High order uniform in time schemes for weakly nonlinear Schrödinger equation and wave turbulence

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