{
  "abstract": "We introduce a novel structure-preserving numerical method for a first-order hyperbolic approximation system, which approximates the solutions of general fourth-order partial differential equations. By employing an implicit-explicit (IMEX) splitting between the stiff and non-stiff terms, we rigorously prove that the proposed scheme is energy-consistent and positivity-preserving under a CFL-type condition. Furthermore, we show that the method remains robustly stable in asymptotic regimes, with a time-step restriction that is entirely independent of the relaxation parameters. Finally, we present a series of numerical examples for thin film equations to validate the theoretical properties and efficacy of the scheme.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.05939",
  "author_total": 2,
  "authors": [
    {
      "name": "Rahul Barthwal"
    },
    {
      "name": "Rahuldev Ghorai"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c4pgdy832y2va.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.05939",
  "fulltext_url": null,
  "id": "c4pgdy832y2va",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.05939",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "2612|Numerical methods for differential equations"
    ]
  ],
  "openalex": "W7212066997",
  "pdf_url": "https://arxiv.org/pdf/2609.05939",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c4pgdy832y2va.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.05939",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.05939"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "A structure-preserving implicit-explicit method for a hyperbolic approximation of fourth-order PDEs",
  "title_text": "A structure-preserving implicit-explicit method for a hyperbolic approximation of fourth-order PDEs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/c4pgdy832y2va",
  "venue": "arXiv",
  "versions": []
}