{
  "abstract": "We develop a fully implicit fast method for semilinear variable-order fractional reaction--diffusion equations with periodic fractional diffusion and exponential-transition Scarpi memory. A Volterra-resolvent analysis establishes local well-posedness and temporal regularity estimates that describe the weak initial singularity. Backward Euler convolution quadrature combined with Fourier pseudospectral discretization achieves mesh-uniform stability and positive-time first-order convergence. To accelerate the scheme, we utilize Cauchy--FFT weight recovery and adaptive blockwise sum-of-exponentials compression, which significantly reduces the cost of history evaluation under local error control. A logarithmic perturbation bound quantifies the effects of weight recovery, history compression, and inexact nonlinear solves, giving tolerance conditions that preserve the convergence order. Numerical experiments confirm the first-order accuracy and demonstrate that the accelerated method efficiently resolves long-time spatial patterns at a substantially reduced computational cost.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.27262",
  "author_total": 2,
  "authors": [
    {
      "name": "Pu Yuan"
    },
    {
      "name": "Paul Zegeling"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/arv7hbj8gn8v0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.27262",
  "fulltext_url": null,
  "id": "arv7hbj8gn8v0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.27262",
  "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": "W7223104301",
  "pdf_url": "https://arxiv.org/pdf/2610.27262",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/arv7hbj8gn8v0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.27262",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.27262"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Convolution Quadrature with Adaptive History Compression for Variable-Order Fractional Reaction--Diffusion Equations",
  "title_text": "Convolution Quadrature with Adaptive History Compression for Variable-Order Fractional Reaction--Diffusion Equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/arv7hbj8gn8v0",
  "venue": "arXiv",
  "versions": []
}