{
  "abstract": "We analyze the long-time stability and convergence of a third-order backward differentiation formula (BDF3) for parabolic equations with exponentially fading memory. The BDF3 scalar resolvent has oscillatory coefficients, so the monotonicity argument used for lower-order formulas in [Math. Comp. 62 (1994) 477-496] does not apply. We instead control memory feedback by the absolute mass of its discrete Green sequence and establish the rigorous stability-constant bounds $23/20<Λ_3<579/500$. A causal third-order memory quadrature with nonnegative assembled weights then yields exponentially weighted stability without a parabolic step-size restriction. With third-order starting values, we prove a uniform-in-time third-order temporal error estimate and extend it to conforming finite elements. Numerical tests confirm the predicted convergence orders and the long-time behavior.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.32364",
  "author_total": 1,
  "authors": [
    {
      "name": "Wenlin Qiu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eq4p53dcqdv7t.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.32364",
  "fulltext_url": null,
  "id": "eq4p53dcqdv7t",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.32364",
  "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|Numerical methods for differential equations"
    ]
  ],
  "openalex": "W7223694809",
  "pdf_url": "https://arxiv.org/pdf/2610.32364",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/eq4p53dcqdv7t.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2610.32364",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.32364"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Long-time stability and convergence of a BDF3 method for a parabolic equation with fading memory",
  "title_text": "Long-time stability and convergence of a BDF3 method for a parabolic equation with fading memory",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/eq4p53dcqdv7t",
  "venue": "arXiv",
  "versions": []
}