{
  "abstract": "The Landau transformation xi = x/s(t) is the usual way to hold a moving boundary in place. It fails for fractional time derivatives because they have no chain rule: the transformed operator gains a nonlocal integral with a closed form only for self-similar fronts. We develop a sharp-interface finite-difference scheme for the conservation-consistent memory-flux fractional Stefan problem on a fixed grid, storing the memory limit h(x) = s^-1(x) as the time each node melts. The front is advanced using an integrated energy balance, with the singular source timed to the sub-step crossing instant. Against a known self-similar solution, the front constant is accurate to 0.02 to 0.11%, whereas competing formulations differ by 17 to 27% at alpha = 0.6. A remaining positivity violation follows from dt/t0 ~ s0^(1 - 2/alpha) and disappears on a front-locked time grid. We also derive two exact solutions with non-power-law fronts: a source-dominated solution and a Mittag-Leffler traveling wave, and verify the scheme against both. Neural-network solvers for moving boundaries are often trained in normalized coordinates; for alpha < 1, this silently changes the problem, while the change vanishes at alpha = 1, where checks are commonly performed. In the classical limit, our scheme is more accurate in 12 ms than a reimplemented moving-boundary network in 177 s.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.04026",
  "author_total": 1,
  "authors": [
    {
      "name": "Conrard Giresse Tetsassi Feugmo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a62dvv1jywh7z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.04026",
  "fulltext_url": null,
  "id": "a62dvv1jywh7z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.04026",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.mtrl-sci"
    ],
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.NA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.04026",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a62dvv1jywh7z.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:25Z",
      "native_id": "2611.04026",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.04026"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.mtrl-sci",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Fixed-grid schemes for fractional moving-boundary problems",
  "title_text": "Fixed-grid schemes for fractional moving-boundary problems",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/a62dvv1jywh7z",
  "venue": "arXiv",
  "versions": []
}