{
  "abstract": "In this paper, we develop a linearly implicit relaxation Crank-Nicolson difference scheme for the two-dimensional space-fractional nonlinear Schrödinger (SFNS) equation, where the fractional Laplacian is approximated by a simple fractional central difference scheme. The proposed scheme is uniquely solvable and conserves discrete mass for general real-valued nonlinear coefficients, and a modified discrete energy in the cubic case. By introducing a modified error system employing a cut-off technique, we establish the optimal-order error estimates without mesh-ratio restriction. Specifically, the primary variable achieves second-order temporal and spatial convergence in the discrete $H_h^{α/2}$-norm, and the relaxation variable satisfies the same convergence in the discrete $L^2$-norm. Some numerical experiments confirm the relevant theoretical results.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.00571",
  "author_total": 2,
  "authors": [
    {
      "name": "Lisen Ding"
    },
    {
      "name": "Dongling Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bfnrzydx4dhxb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00571",
  "fulltext_url": null,
  "id": "bfnrzydx4dhxb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00571",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.00571",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bfnrzydx4dhxb.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.00571",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00571"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Unconditional optimal convergence of a relaxation Crank-Nicolson difference scheme for 2D space-fractional NLS",
  "title_text": "Unconditional optimal convergence of a relaxation Crank-Nicolson difference scheme for 2D space-fractional NLS",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/bfnrzydx4dhxb",
  "venue": "arXiv",
  "versions": []
}