{
  "abstract": "We develop stability and error estimates for multistep convolution quadrature (CQ) under general radial bounds on the Laplace symbol. Instead of the classical single-power condition $|F(z)|\\leq M|z|^{-μ}$, we assume $|F(z)|\\leq CΦ(|z|)$, where $Φ$ is positive, continuous and regularly varying at zero and infinity. For strongly $A(α)$-stable multistep methods, we derive error estimates and stability estimates for the CQ weights, as well as error bounds for power-type inputs $g_β(t)=t^{\\beta1}/Γ(β)$ with $β>0$. These estimates explicitly retain the dependence on the memory law through the factor $Φ(t_n^{-1})$. The framework accommodates symbols whose behavior cannot be described by a global single-power. It also preserves logarithmic and multiscale factors that would be lost under a coarser power bounds. Then we apply the to fractional viscoelastic, distributed-order, and logarithmic-power memory models. Numerical experiments with backward Euler and second-order backward differentiation CQ confirm the expected temporal convergence orders for direct responses. A distributed-order PDE further illustrates temporal convergence for smooth and nonsmooth initial data.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.23163",
  "author_total": 2,
  "authors": [
    {
      "name": "Jingchuang Ren"
    },
    {
      "name": "Haibin Su"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4et1qxvwfke9e.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.23163",
  "fulltext_url": null,
  "id": "4et1qxvwfke9e",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.23163",
  "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",
      "2611|Fractional Differential Equations Solutions"
    ]
  ],
  "openalex": "W7222982657",
  "pdf_url": "https://arxiv.org/pdf/2610.23163",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4et1qxvwfke9e.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2610.23163",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.23163"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Stability and Error Estimates for Convolution Quadrature under Radial Symbol Bounds",
  "title_text": "Stability and Error Estimates for Convolution Quadrature under Radial Symbol Bounds",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/4et1qxvwfke9e",
  "venue": "arXiv",
  "versions": []
}