Superconvergence points of Hermite spectral interpolation

[2507.15350] Superconvergence points of Hermite spectral interpolation Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Numerical Analysis arXiv:2507.15350 (math) [Submitted on 21 Jul 2025 ( v1 ), last revised 7 Aug 2026 (this version, v2)] Title: Superconvergence points of Hermite spectral interpolation Authors: Haiyong Wang , Zhimin Zhang View a PDF of the paper titled Superconvergence points of Hermite spectral interpolation, by Haiyong Wang and Zhimin Zhang View PDF HTML (experimental) Abstract: Hermite spectral method plays an important role in the numerical simulation of various partial differential equations (PDEs) on unbounded domains. In this work, we study the superconvergence properties of Hermite spectral interpolation, i.e., interpolation at the zeros of Hermite polynomials in the space spanned by Hermite functions. We identify the points at which the convergence rates of the first- and second-order derivatives of the interpolant converge faster. We further extend the analysis to the Hermite spectral collocation method in solving differential equations and identify the superconvergence points both for function and derivative values. Numerical examples are provided to confirm the analysis of superconvergence points. Comments: J. Sci. Comput., to appear Subjects: Numerical Analysis (math.NA) MSC classes: 41A05, 41A25, 65N35, 65D05 Cite as: arXiv:2507.15350 [math.NA] (or arXiv:2507.15350v2 [math.NA] for this version) https://doi.org/10.48550/arXiv.2507.15350 Focus to learn more arXiv-issued DOI via DataCite Journal reference: 109, article number 15, 2026 Related DOI : https://doi.org/10.1007/s10915-026-03436-z Focus to learn more DOI(s) linking to related resources Submission history From: Haiyong Wang [ view email ] [v1] Mon, 21 Jul 2025 08:01:46 UTC (883 KB) [v2] Fri, 7 Aug 2026 04:16:50 UTC (1,060 KB) Full-text links: Access Paper: View a PDF of the paper titled Superconvergence points of Hermite spectral interpolation, by Haiyong Wang and Zhimin Zhang View PDF HTML (experimental) TeX Source view license Current browse context: math.NA < prev | next > new | recent | 2025-07 Change to browse by: cs cs.NA math 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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