A second-order implicit difference scheme for the nonlinear time-space fractional Schrodinger equation

被引：13
|
作者：
Fei, Mingfa [1 ,2 ]
Wang, Nan [3 ]
Huang, Chengming [4 ]
Ma, Xiaohua [5 ]
机构：
[1] Changsha Univ, Sch Comp Engn & Appl Math, Changsha 410022, Peoples R China
[2] Changsha Univ, Hunan Prov Key Lab Ind Internet Technol & Secur, Changsha 410022, Peoples R China
[3] Zhengzhou Univ, Sch Math & Stat, Zhengzhou 450001, Peoples R China
[4] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Peoples R China
[5] Changsha Univ Sci & Technol, Sch Math & Stat, Changsha 410022, Peoples R China
来源：
APPLIED NUMERICAL MATHEMATICS | 2020年 / 153卷
基金：
中国博士后科学基金;
关键词：
Time-space fractional Schrodinger equation; Caputo derivative; Riesz fractional derivative; L2-1(sigma) formula; Convergence; Unique solvability; FINITE-ELEMENT-METHOD; SPECTRAL METHOD; WELL-POSEDNESS;
D O I：
10.1016/j.apnum.2020.03.004
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we develop an implicit difference method for solving the nonlinear time-space fractional Schrodinger equation. The scheme is constructed by using the L2-1(sigma) formula to approximate the Caputo fractional derivative, while the weighted and shifted Grunwald formula is adopted for the spatial discretization. The stability and unique solvability of the difference scheme are analyzed in detail. Moreover, we prove that the numerical solution is convergent with second-order accuracy in both temporal and spatial directions. Finally, a linearized iterative algorithm is provided and some numerical tests are presented to validate our theoretical results. (C) 2020 IMACS. Published by Elsevier B.V. All rights reserved.
引用
收藏
页码：399 / 411
页数：13
相关论文
共 50 条
  • [41] A linearized and second-order unconditionally convergent scheme for coupled time fractional Klein-Gordon-Schrodinger equation
    Lyu, Pin
    Vong, Seakweng
    NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2018, 34 (06) : 2153 - 2179
  • [42] On a class of second-order nonlinear difference equation
    Li Dongsheng
    Zou Shuliang
    Liao Maoxin
    Advances in Difference Equations, 2011
  • [43] Second-order explicit difference schemes for the space fractional advection diffusion equation
    Li, Wei
    Li, Can
    APPLIED MATHEMATICS AND COMPUTATION, 2015, 257 : 446 - 457
  • [44] On a class of second-order nonlinear difference equation
    Li Dongsheng
    Zou Shuliang
    Liao Maoxin
    ADVANCES IN DIFFERENCE EQUATIONS, 2011, : 1 - 9
  • [45] Time-space fractional Schrodinger like equation with a nonlocal term
    Jiang, X. Y.
    EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS, 2011, 193 (01): : 61 - 70
  • [46] A second-order difference scheme for the nonlinear time-fractional diffusion-wave equation with generalized memory kernel in the presence of time delay
    Alikhanov, Anatoly A.
    Asl, Mohammad Shahbazi
    Huang, Chengming
    Khibiev, Aslanbek
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2024, 438
  • [47] A conservative linearized difference scheme for the nonlinear fractional Schrodinger equation
    Wang, Pengde
    Huang, Chengming
    NUMERICAL ALGORITHMS, 2015, 69 (03) : 625 - 641
  • [48] Crank-Nicolson Finite Difference Scheme for Time-Space Fractional Diffusion Equation
    Takale, Kalyanrao C.
    Sangvikar , Veena V.
    MATHEMATICS AND COMPUTING, ICMC 2022, 2022, 415 : 701 - 710
  • [49] A second-order time-discretization scheme for a system of nonlinear Schrodinger equations
    Sasaki, Takiko
    PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 2014, 90 (01) : 15 - 20
  • [50] A fourth-order implicit-explicit scheme for the space fractional nonlinear Schrodinger equations
    Khaliq, A. Q. M.
    Liang, X.
    Furati, K. M.
    NUMERICAL ALGORITHMS, 2017, 75 (01) : 147 - 172
12345