Optimal error analysis of the Alikhanov formula for a time-fractional Schrodinger equation

被引：7
|
作者：
Zhao, Guoye [1 ]
An, Na [1 ]
Huang, Chaobao [2 ]
机构：
[1] Shandong Normal Univ, Sch Math & Stat, Jinan 250014, Peoples R China
[2] Shandong Univ Finance & Econ, Sch Math & Quantitat Econ, Jinan 250014, Peoples R China
来源：
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING | 2023年 / 69卷 / 01期
基金：
中国国家自然科学基金;
关键词：
lime-fractional Schrodinger equations; The Alikhanov formula; Finite element methods; Graded meshes; Weak singularity; SCHEMES;
D O I：
10.1007/s12190-022-01733-y
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we have developed a fully discrete Alikhanov finite element method to solve the time-fractional Schrodinger equation with non-smooth solution. The proposed scheme uses the Alikhanov formula on graded meshes to approximate the Caputo fractional derivative in temporal direction and the standard finite element method in spatial direction. Furthermore, the L-2(Omega)-norm stability and the optimal convergent result for the computed solution are derived. Finally, a numerical example is presented to verify the accuracy of the proposed scheme.
引用
收藏
页码：159 / 170
页数：12
相关论文
共 50 条
  • [21] α-robust error analysis of a mixed finite element method for a time-fractional biharmonic equation
    Chaobao Huang
    Martin Stynes
    Numerical Algorithms, 2021, 87 : 1749 - 1766
  • [22] ERROR ANALYSIS OF A FINITE DIFFERENCE METHOD ON GRADED MESHES FOR A TIME-FRACTIONAL DIFFUSION EQUATION
    Stynes, Martin
    O'Riordan, Eugene
    Luis Gracia, Jose
    SIAM JOURNAL ON NUMERICAL ANALYSIS, 2017, 55 (02) : 1057 - 1079
  • [23] α-robust error analysis of a mixed finite element method for a time-fractional biharmonic equation
    Huang, Chaobao
    Stynes, Martin
    NUMERICAL ALGORITHMS, 2021, 87 (04) : 1749 - 1766
  • [24] Optimal Convergence Rates in Time-Fractional Discretisations: the L1, L1 and Alikhanov Schemes
    Zhou, Yongtao
    Stynes, Martin
    EAST ASIAN JOURNAL ON APPLIED MATHEMATICS, 2022, 12 (03) : 503 - 520
  • [25] Optimal error bound and simplified Tikhonov regularization method for a backward problem for the time-fractional diffusion equation
    Wang, Jun-Gang
    Wei, Ting
    Zhou, Yu-Bin
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2015, 279 : 277 - 292
  • [26] On Tikhonov's method and optimal error bound for inverse source problem for a time-fractional diffusion equation
    Nguyen Minh Dien
    Dinh Nguyen Duy Hai
    Tran Quoc Viet
    Dang Duc Trong
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2020, 80 (01) : 61 - 81
  • [27] Error analysis of a fully discrete scheme for time fractional Schrodinger equation with initial singularity
    Zhang, Jun
    Chen, Hu
    Sun, Tao
    Wang, Jinrong
    INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2020, 97 (08) : 1636 - 1647
  • [28] Optical solitons of a time-fractional higher-order nonlinear Schrodinger equation
    Fang, Jia-Jie
    Dai, Chao-Qing
    OPTIK, 2020, 209
  • [29] Fractional Landweber Iterative Regularization Method for Solving the Inverse Problem of Time-Fractional Schrodinger Equation
    Gao, Yinxia
    Li, Dungang
    Yang, Fan
    Li, Xiaoxiao
    SYMMETRY-BASEL, 2022, 14 (10):
  • [30] Non-polynomial spline method for the time-fractional nonlinear Schrodinger equation
    Li, Mingzhu
    Ding, Xiaohua
    Xu, Qiang
    ADVANCES IN DIFFERENCE EQUATIONS, 2018,
12345