Skip to content
DraconiticResearch
Search Sources API
197,768 studies31 sourcesUpdated 27 min ago
Peer-reviewedCC BY 4.0Mathematics

Numerical Simulation of the Time-Fractional Nonlinear Schrödinger Equation and the Time-Fractional Schrödinger–Poisson System

  • Omid Nikan1
  • Zakieh Avazzadeh2
  1. 1School of Mathematics and Computer Science, Iran University of Science and Technology, Narmak, Tehran 16846-13114, Iran
  2. 2Stony Brook Institute, Anhui University, Hefei 230601, China
Open at sourceDOICite

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.

Related

  1. Uniqueness and structure-preserving numerical simulations for an Ultrahyperbolic Schrödinger equation
    Özlem Kaytmaz, Muhammed Hasdemir
    Scientific ReportsPeer-reviewedCC BY-NC-ND 4.0Full textMathematical physicsCrossref
  2. Numerical approximation of nonlinear fractional dynamical systems for coastal wave modeling: rigorous analysis of convergence and computational efficiency
    Rabeb Sidaoui, Faten H. Damag, Amin Saif +1
    Scientific ReportsPeer-reviewedCC BY-NC-ND 4.0Full textGeneral mathematicsCrossref
  3. The Calderón problem for the fractional Schrödinger equation at a single point
    Bastian Harrach, Yi-Hsuan Lin
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsarXiv
  4. Orbital stability of standing waves for defocusing fractional nonlinear Schrödinger equations with a delta potential
    Ramón G. Plaza, Miguel A. Sánchez-Alcántara
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  5. Global well-posedness for the derivative nonlinear Schrödinger equation on the circle
    Hajer Bahouri, Galina Perelman
    HALPreprintCC BY-NC-ND 4.0Full textAnalysis & PDEsHALarXiv

Cite

BibTeXRIS
BibTeX
@article{nikan2026numerical,
  title = {{Numerical Simulation of the Time-Fractional Nonlinear Schrödinger Equation and the Time-Fractional Schrödinger–Poisson System}},
  author = {Omid Nikan and Zakieh Avazzadeh},
  journal = {Mathematics},
  year = {2026},
  month = oct,
  doi = {10.3390/math14203731},
  url = {https://www.mdpi.com/2227-7390/14/20/3731},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Numerical Simulation of the Time-Fractional Nonlinear Schrödinger Equation and the Time-Fractional Schrödinger–Poisson System
AU  - Omid Nikan
AU  - Zakieh Avazzadeh
PY  - 2026
DA  - 2026/10/14
JO  - Mathematics
DO  - 10.3390/math14203731
UR  - https://www.mdpi.com/2227-7390/14/20/3731
AB  - 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.
SN  - 2227-7390
ER  -