{
  "abstract": "We develop and analyze a class of Hermite-type methods for linear advection-diffusion equations in the case of one-dimensional periodic domains. The methods evolve both nodal values and cell averages and are therefore referred to as hybrid-variable (HV) methods. Using Hermite interpolation theory, we construct the HV methods to arbitrary order of accuracy, and prove that the method is supraconvergent in the sense that the spatial order of accuracy can be up to two orders larger than the local truncation error. In the second part, we prove all central HV methods for linear diffusion equations and linear advection-diffusion equations are stable at the semi-discretized level. Next, we prove the convergence of all stable HV schemes and provide error estimate in the discrete $L^2$-norm of the semi-discretized solution, which extends the supraconvergence from a single mode to all sufficiently smooth initial data. The theoretical predictions on the accuracy and stability of the methods are verified by extensive numerical tests.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14545",
  "author_total": 1,
  "authors": [
    {
      "name": "Xianyi Zeng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5xdc4bn3c8003.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14545",
  "fulltext_url": null,
  "id": "5xdc4bn3c8003",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14545",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "2612|Differential Equations and Numerical Methods"
    ]
  ],
  "openalex": "W7213284369",
  "pdf_url": "https://arxiv.org/pdf/2609.14545",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5xdc4bn3c8003.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2609.14545",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14545"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "On a class of supraconvergent Hermite-type methods for advection-diffusion equations",
  "title_text": "On a class of supraconvergent Hermite-type methods for advection-diffusion equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/5xdc4bn3c8003",
  "venue": "arXiv",
  "versions": []
}