Improved error estimates for low-regularity integrators using space-time bounds

[2503.22621] Improved error estimates for low-regularity integrators using space-time bounds Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Numerical Analysis arXiv:2503.22621 (math) [Submitted on 28 Mar 2025 ( v1 ), last revised 14 Apr 2026 (this version, v2)] Title: Improved error estimates for low-regularity integrators using space-time bounds Authors: Maximilian Ruff View a PDF of the paper titled Improved error estimates for low-regularity integrators using space-time bounds, by Maximilian Ruff View PDF HTML (experimental) Abstract: We prove optimal convergence rates for certain low-regularity integrators applied to the one-dimensional periodic nonlinear Schrödinger and wave equations under the assumption of $H^1$ solutions. For the Schrödinger equation we analyze the exponential-type scheme proposed by Ostermann and Schratz in 2018, whereas in the wave case we treat the corrected Lie splitting proposed by Li, Schratz, and Zivcovich in 2023. We show that the integrators converge with their full order of one and two, respectively. In this situation only fractional convergence rates were previously known. The crucial ingredients in the proofs are known space-time bounds for the solutions to the corresponding linear problems. More precisely, in the Schrödinger case we use the $L^4$ Strichartz inequality, and for the wave equation a null form estimate. To our knowledge, this is the first time that a null form estimate is exploited in numerical analysis. We apply the estimates for continuous time, thus avoiding potential losses resulting from discrete-time estimates. Comments: Revised version, accepted for publication in IMA J. Numer. Anal Subjects: Numerical Analysis (math.NA) ; Analysis of PDEs (math.AP) MSC classes: 65M15 (Primary) 35L71, 35Q55, 65M12 (Secondary) Cite as: arXiv:2503.22621 [math.NA] (or arXiv:2503.22621v2 [math.NA] for this version) https://doi.org/10.48550/arXiv.2503.22621 Focus to learn more arXiv-issued DOI via DataCite Related DOI : https://doi.org/10.1093/imanum/drag045 Focus to learn more DOI(s) linking to related resources Submission history From: Maximilian Ruff [ view email ] [v1] Fri, 28 Mar 2025 17:14:16 UTC (16 KB) [v2] Tue, 14 Apr 2026 10:22:53 UTC (23 KB) Full-text links: Access Paper: View a PDF of the paper titled Improved error estimates for low-regularity integrators using space-time bounds, by Maximilian Ruff View PDF HTML (experimental) TeX Source view license Current browse context: math.NA < prev | next > new | recent | 2025-03 Change to browse by: cs cs.NA math math.AP References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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