Stability and convergence of the space fractional variable-order Schrödinger equation

被引：0
|
作者：
Abdon Atangana
Alain H Cloot
机构：
[1] University of the Free State,Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences
[2] University of the Free State,Department of Mathematics and Applied Mathematics
来源：
Advances in Difference Equations | / 2013卷
关键词：
Schrödinger equation; variable-order derivative; Crank-Nicholson scheme; convergence; stability;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The space fractional Schrödinger equation was further extended to the concept of space fractional variable-order derivative. The generalized equation is very difficult to handle analytically. We solved the generalized equation numerically via the Crank-Nicholson scheme. The stability and the convergence of the space fractional variable-order Schrödinger equation were presented in detail.
引用
收藏
相关论文
共 50 条
  • [41] Stability analysis and dispersive optical solitons of fractional Schrödinger–Hirota equation
    Sonia Akram
    Jamshad Ahmad
    Shafqat Ur Rehman
    Tayyaba Younas
    Optical and Quantum Electronics, 2023, 55
  • [42] Stability of periodic waves for the defocusing fractional cubic nonlinear Schrõdinger equation
    Borluk, Handan
    Muslu, Gulcin M.
    Natali, Fabio
    COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2024, 133
  • [43] On Variable-Order Fractional Discrete Neural Networks: Solvability and Stability
    Hioual, Amel
    Ouannas, Adel
    Oussaeif, Taki-Eddine
    Grassi, Giuseppe
    Batiha, Iqbal M.
    Momani, Shaher
    FRACTAL AND FRACTIONAL, 2022, 6 (02)
  • [44] A space-time DG method for the Schrödinger equation with variable potential
    Gomez, Sergio
    Moiola, Andrea
    ADVANCES IN COMPUTATIONAL MATHEMATICS, 2024, 50 (02)
  • [45] Symmetry of the Schrödinger Equation with Variable Potential
    Wilhelm Fushchych
    Zoya Symenoh
    Ivan Tsyfra
    Journal of Nonlinear Mathematical Physics, 1998, 5 : 13 - 22
  • [46] FINITE DIFFERENCE SCHEMES FOR VARIABLE-ORDER TIME FRACTIONAL DIFFUSION EQUATION
    Sun, Hongguang
    Chen, Wen
    Li, Changpin
    Chen, Yangquan
    INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2012, 22 (04):
  • [47] Legendre wavelets optimization method for variable-order fractional Poisson equation
    Heydari, Mohammad Hossein
    Avazzadeh, Zakieh
    CHAOS SOLITONS & FRACTALS, 2018, 112 : 180 - 190
  • [48] Numerical Method for the Variable-Order Fractional Filtration Equation in Heterogeneous Media
    Alimbekova, Nurlana
    Bakishev, Aibek
    Berdyshev, Abdumauvlen
    FRACTAL AND FRACTIONAL, 2024, 8 (11)
  • [49] Analysis and numerical solution of a nonlinear variable-order fractional differential equation
    Hong Wang
    Xiangcheng Zheng
    Advances in Computational Mathematics, 2019, 45 : 2647 - 2675
  • [50] Numerical algorithm for the variable-order Caputo fractional functional differential equation
    Bhrawy, A. H.
    Zaky, M. A.
    NONLINEAR DYNAMICS, 2016, 85 (03) : 1815 - 1823
12345