{
  "abstract": "We develop an immersed interface finite difference method for a one-dimensional nonlinear parabolic interface problem with jump condition \\[ [u]_α=λu^+u^-. \\] The method combines a Crank--Nicolson immersed interface discretization with an \\(s\\)-parameter reduction of the nonlinear interface condition, thereby reducing the nonlinear coupling to a scalar quadratic equation. We also discuss two different viewpoints for combining Newton iteration with immersed interface discretization, namely the IIM--Newton and Newton--IIM formulations. Numerical experiments are presented to illustrate the behavior and accuracy of the method.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.30062",
  "author_total": 2,
  "authors": [
    {
      "name": "So-Hsiang Chou"
    },
    {
      "name": "Patrick Nyadjo Fonga"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/77ecannn1fv89.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.30062",
  "fulltext_url": null,
  "id": "77ecannn1fv89",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.30062",
  "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",
      "2206|Advanced Numerical Methods in Computational Mathematics"
    ]
  ],
  "openalex": "W7204880394",
  "pdf_url": "https://arxiv.org/pdf/2608.30062",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/77ecannn1fv89.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.30062",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.30062"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "An Immersed Interface Method for Parabolic Interface Problems with Nonlinear Jump Conditions",
  "title_text": "An Immersed Interface Method for Parabolic Interface Problems with Nonlinear Jump Conditions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/77ecannn1fv89",
  "venue": "arXiv",
  "versions": []
}