{
  "abstract": "In this paper, we develop a novel class of high-order uniformly accurate exponential integrators for charged-particle dynamics under strong magnetic field. The small parameter $0<\\varepsilon\\ll 1$ induces rapid temporal oscillations, rendering traditional numerical methods prohibitively expensive due to severe step-size restrictions. To address this issue, a linearization technology that introduces auxiliary polynomial variables is employed to recast the original charged-particle dynamics as a higher-dimensional system. Classical exponential integrators are subsequently applied to this augmented formulation, which inherently carries richer structural information, thereby yielding a family of uniformly accurate exponential integrators that can reach arbitrarily high order without requiring any order conditions. For strong magnetic fields under the maximal-ordering scaling, we rigorously establish through algebraic techniques that the schemes with auxiliary polynomial variables of degree $k\\geq2$ achieve an improved position error bound of $\\mathcal{O}(\\min\\{\\varepsilon^{k+1}h,\\varepsilon h^{k+1}\\})$ and a uniform velocity error bound of $\\mathcal{O}(\\min\\{\\varepsilon^{k}h,h^{k+1}\\})$, where $h$ denotes the time-step size. Under the additional condition that the magnetic field gradient vanishes at the origin, these bounds sharpen to $\\mathcal{O}(\\min\\{\\varepsilon^{k+2},\\varepsilon h^{k+1}\\})$ and $\\mathcal{O}(\\min\\{\\varepsilon^{k+1},h^{k+1}\\})$ for the position and velocity, respectively, for $k\\geq1$. The same sharper bounds hold for constant strong magnetic fields. Numerical experiments confirm the advantages of the proposed methods.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.04478",
  "author_total": 3,
  "authors": [
    {
      "name": "Lina Wang"
    },
    {
      "name": "Bin Wang"
    },
    {
      "name": "Beibei Zhu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9mdqp0fz06axb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.04478",
  "fulltext_url": null,
  "id": "9mdqp0fz06axb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.04478",
  "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": "W7163589346",
  "pdf_url": "https://arxiv.org/pdf/2606.04478",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9mdqp0fz06axb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2606.04478",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.04478"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "A novel class of high-order uniformly accurate exponential integrators with local linear extension for the charged-particle dynamics under strong magnetic field",
  "title_text": "A novel class of high-order uniformly accurate exponential integrators with local linear extension for the charged-particle dynamics under strong magnetic field",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/9mdqp0fz06axb",
  "venue": "arXiv",
  "versions": []
}