{
  "abstract": "Splitting the exponential and exponential-like functions can significantly reduce the overall computational cost of exponential integrators, providing a strong motivation for their rigorous analysis. In this paper, we analyze splitting errors for two noncommuting unbounded operators and derive new representations that include the popular Lie--Trotter and Strang cases. Moreover, within the abstract framework of strongly continuous semigroups, we prove the convergence of a split version of the exponential Euler method and a second-order exponential Runge--Kutta method for semilinear problems. Numerical experiments on a nonlinear dispersive equation and a diffusion--reaction equation demonstrate the theoretical findings, stability properties, and efficiency of the proposed split exponential integrators compared to the state of the art.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.07989",
  "author_total": 3,
  "authors": [
    {
      "name": "Luca Battestini"
    },
    {
      "name": "Marco Caliari"
    },
    {
      "name": "Fabio Cassini"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cz4evz8a1mnmc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.07989",
  "fulltext_url": null,
  "id": "cz4evz8a1mnmc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.07989",
  "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",
      "2612|Numerical methods for differential equations"
    ]
  ],
  "openalex": "W7221004716",
  "pdf_url": "https://arxiv.org/pdf/2610.07989",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cz4evz8a1mnmc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2610.07989",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.07989"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Analysis of split exponential integrators for semilinear problems with noncommuting operators",
  "title_text": "Analysis of split exponential integrators for semilinear problems with noncommuting operators",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/cz4evz8a1mnmc",
  "venue": "arXiv",
  "versions": []
}