{
  "abstract": "The L2 discretization of the Caputo derivative is attractive for its high-order accuracy, but its analysis on nonuniform temporal meshes is complicated due to the lack of a monotone structure in the discrete coefficients. This difficulty is particularly significant for deriving sharp $L^2$ error estimates in the presence of the typical weak singularity of subdiffusion solutions near the initial time. In this work, we develop a coefficient-recombination framework for the L2 method on nonuniform meshes. Under the adjacent step-ratio condition $0.86\\le ρ_k\\le 1.16$, $k\\ge2$, we prove that the recombined L2 coefficients are positive and monotone. A key ingredient is a cross-row recombination technique: with the recombination parameter associated with a fixed time level, all coefficient rows retain positivity and monotonicity, which allows us to close an induction for the $L^2$ error analysis. For solutions exhibiting the standard initial weak singularity, we derive an $L^2$ error estimate on nonuniform meshes satisfying the step-ratio condition. On a modified graded mesh with grading parameter $r>1$, the estimate yields the convergence rate $\\mathcal{O}\\!\\left(N^{-\\min\\{rα,\\,3-α\\}}\\right)$, and hence recovers the optimal order $\\mathcal{O}(N^{-(3-α)})$ whenever $r\\ge(3-α)/α$. Numerical experiments on random nonmonotone meshes and modified graded meshes confirm the theoretical estimates.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.39642",
  "author_total": 4,
  "authors": [
    {
      "name": "Chaoyu Quan"
    },
    {
      "name": "Shangyu Wang"
    },
    {
      "name": "Shijie Wang"
    },
    {
      "name": "Jiang Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/amyyrwmrjb2dk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.39642",
  "fulltext_url": null,
  "id": "amyyrwmrjb2dk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.39642",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.39642",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/amyyrwmrjb2dk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.39642",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.39642"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Coefficient Recombination and Error Estimates for the L2 Method for Subdiffusion on Nonuniform Meshes",
  "title_text": "Coefficient Recombination and Error Estimates for the L2 Method for Subdiffusion on Nonuniform Meshes",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/amyyrwmrjb2dk",
  "venue": "arXiv",
  "versions": []
}