Superconvergence of Strang splitting for NLS in $T^d$
type: Dataset
description: In this paper we investigate the convergence properties of semi-discretized approximations by Strang splitting method applied to fast-oscillating nonlinear Schr¨odinger equations. In a first step and for further use, we briefly adapt a known convergence result for Strang method in the context of NLS on $T^d$ for a large class of nonlinearities. In a second step, we examine how errors depend on the length of the period $\varepsilon$, the solutions being considered on intervals of fixed length (independent of the period). Our main contribution is to show that Strang splitting with constant step-sizes is unexpectedly more accurate by a factor $\varepsilon$ as compared to established results when the step-size is chosen as an integer fraction of the period, owing to an averaging effect.
issued: 2026-05-06T02:53:46.695578
language: en
modified: 2026-05-06T02:53:46.695583
contact point: Organization
  fn: CCSD
keyword: averaging
keyword: highly-oscillatory-systems
keyword: infoeu-reposemanticspreprint
keyword: mathmath-namathematics-mathnumerical-analysis-mathna
keyword: nonlinear
keyword: partial-differential-equation
keyword: preprints-working-papers-
keyword: schrodinger-equation
keyword: splitting-schemes
keyword: strang-splitting
landing page: https://inria.hal.science/hal-00956714

Superconvergence of Strang splitting for NLS in $T^d$
type: Distribution
format: HTML
issued: 2026-05-06T02:53:46.697728
modified: 2026-05-06T02:53:46.677632
access URL: https://inria.hal.science/hal-00956714

test_moissonnage_selune
type: Agent