{
  "abstract": "This paper presents an efficient localized meshless method for solving the nonlinear time-fractional Schrödinger equation and the time-fractional Schrödinger–Poisson system. The proposed approach consists of two main steps. First, the Caputo time-fractional derivative is approximated using the L1 formula, which has an accuracy of order O(δt2−β) for 0<β<1. The spatial derivatives in the coupled equations are then discretized using a localized radial basis function Hermite finite-difference (LRBF-HFD) method. In this approach, the Laplacian operator is approximated on small overlapping neighborhoods, thereby avoiding the large and ill-conditioned systems arising from global RBF methods. Numerical experiments are presented to confirm the accuracy and reliability of the proposed method.",
  "abstract_shown": true,
  "affiliations": [
    "School of Mathematics and Computer Science, Iran University of Science and Technology, Narmak, Tehran 16846-13114, Iran",
    "Stony Brook Institute, Anhui University, Hefei 230601, China"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Omid Nikan",
      "orcid": "0000-0003-3041-8726"
    },
    {
      "affs": [
        1
      ],
      "name": "Zakieh Avazzadeh",
      "orcid": "0000-0003-2257-1798"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ab8ktwp6zfazp.bib",
  "cited_by": 0,
  "doi": "10.3390/math14203731",
  "fulltext_url": null,
  "id": "ab8ktwp6zfazp",
  "issns": [
    "2227-7390"
  ],
  "landing_url": "https://www.mdpi.com/2227-7390/14/20/3731",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2611|Fractional Differential Equations Solutions"
    ]
  ],
  "openalex": "W7213446005",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/ab8ktwp6zfazp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:29Z",
      "native_id": "10.3390/math14203731",
      "source": "crossref",
      "url": "https://www.mdpi.com/2227-7390/14/20/3731"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2611|Fractional Differential Equations Solutions",
      "subfield": "general"
    }
  ],
  "title": "Numerical Simulation of the Time-Fractional Nonlinear Schrödinger Equation and the Time-Fractional Schrödinger–Poisson System",
  "title_text": "Numerical Simulation of the Time-Fractional Nonlinear Schrödinger Equation and the Time-Fractional Schrödinger–Poisson System",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:29Z",
  "url": "https://research.draconitic.com/paper/ab8ktwp6zfazp",
  "venue": "Mathematics",
  "versions": []
}