{
  "abstract": "Numerical experiments reported by Quan and Wu [SIAM J Numer Anal 61 (2023) 2106-2132] show that the observed temporal convergence rates of nonuniform L2 methods for subdiffusion models are not consistent with the theoretically predicted order $3-α$. This discrepancy suggests that a more refined analysis is needed and motivates the development of a nonuniform BDF3-L2 method for the subdiffusion equation. To account for the initial solution singularity, we employ the multiscale solution decomposition to decompose the original solution and approximate a smoother unknown variable that satisfies the subdiffusion model with a smoother source term. The resulting formulation, however, involves restrictive high-order boundary conditions on the source term and initial data. To overcome this difficulty, we introduce a spectral truncation technique that requires only slightly stronger regularity of the data and a controllable truncation error. We establish high-order regularity estimates of the solution to the truncated problem and develop a nonuniform BDF3-L2 method for its numerical approximation, based on which we derive a rigorous error estimate of temporal convergence order $2+α$. Numerical experiments are carried out to substantiate the theoretical findings.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.02178",
  "author_total": 4,
  "authors": [
    {
      "name": "Wenlin Qiu"
    },
    {
      "name": "Kexin Li"
    },
    {
      "name": "Yiqun Li"
    },
    {
      "name": "Hao Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dpy6ykam4q6ww.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.02178",
  "fulltext_url": null,
  "id": "dpy6ykam4q6ww",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.02178",
  "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": "W7207833050",
  "pdf_url": "https://arxiv.org/pdf/2609.02178",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dpy6ykam4q6ww.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:20Z",
      "native_id": "2609.02178",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.02178"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Error estimate of the nonuniform BDF3-L2 method for subdiffusion equations via multiscale solution decomposition",
  "title_text": "Error estimate of the nonuniform BDF3-L2 method for subdiffusion equations via multiscale solution decomposition",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/dpy6ykam4q6ww",
  "venue": "arXiv",
  "versions": []
}