Open AccessError estimates at low regularity of splitting schemes for NLS
Author(s) -
Alexander Ostermann,
Frédéric Rousset,
Katharina Schratz
Publication year - 2021
Publication title -
mathematics of computation
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.95
H-Index - 103
eISSN - 1088-6842
pISSN - 0025-5718
DOI - 10.1090/mcom/3676
Subject(s) - algorithm , computer science , annotation , artificial intelligence
We study a filtered Lie splitting scheme for the cubic nonlinear Schrödinger equation. We establish error estimates at low regularity by using discrete Bourgain spaces. This allows us to handle data in H s H^s with 0 > s > 1 0>s>1 overcoming the standard stability restriction to smooth Sobolev spaces with index s > 1 / 2 s>1/2 . More precisely, we prove convergence rates of order τ s / 2 \tau ^{s/2} in L 2 L^2 at this level of regularity.