{
  "abstract": "This paper extends the convergence analysis of explicit exponential Runge--Kutta methods for linear parabolic problems $u'(t) + Au(t) = Bu(t)$, where $A$ generates an analytic semigroup and $B$ is relatively bounded with respect to $A$, from the third-order case to fourth-order schemes. By establishing the global error recursion relation and extending the defect-based analytical framework, we identify the terms responsible for stiff order reduction when $A$ and $B$ do not commute. Numerical experiments are performed on a non-commuting advection-diffusion problem to validate the theoretical results. Numerical tests using the classical four-stage, fourth-order schemes of Krogstad and Strehmel \\& Weiner exhibit an observed convergence order of approximately 2.75, which matches the theoretical prediction from the convergence analysis.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09932",
  "author_total": 3,
  "authors": [
    {
      "name": "Thi Tam Dang"
    },
    {
      "name": "Pablo Alexei Gazca-Orozco"
    },
    {
      "name": "Trung Hau Hoang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f1yx3a01stkp1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09932",
  "fulltext_url": null,
  "id": "f1yx3a01stkp1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09932",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "2612|Numerical methods for differential equations"
    ]
  ],
  "openalex": "W7212143826",
  "pdf_url": "https://arxiv.org/pdf/2609.09932",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f1yx3a01stkp1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:15Z",
      "native_id": "2609.09932",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09932"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Order Reduction of Exponential Runge--Kutta Methods: Fourth-Order Schemes for Non-Commuting Operators",
  "title_text": "Order Reduction of Exponential Runge--Kutta Methods: Fourth-Order Schemes for Non-Commuting Operators",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/f1yx3a01stkp1",
  "venue": "arXiv",
  "versions": []
}