A fourth-order linearized difference scheme for the coupled space fractional Ginzburg-Landau equation

被引：4
作者：
Xu, Yuan [1 ]
Zeng, Jiali [1 ]
Hu, Shuanggui [1 ,2 ]
机构：
[1] Cent S Univ, Sch Math & Stat, Changsha, Hunan, Peoples R China
[2] Cent S Univ, Sch Geosci & Infophys, Changsha, Hunan, Peoples R China
来源：
ADVANCES IN DIFFERENCE EQUATIONS | 2019年 / 2019卷 / 01期
基金：
美国国家科学基金会;
关键词：
Ginzburg-Landau equation; Fractional Laplacian; Pointwise error estimate; Unconditional stability; Fourth-order convergence; NONLINEAR SCHRODINGER-EQUATIONS; FINITE-ELEMENT-METHOD; NUMERICAL-METHODS;
D O I：
10.1186/s13662-019-2389-5
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, the coupled space fractional Ginzburg-Landau equations are investigated numerically. A linearized semi-implicit difference scheme is proposed. The scheme is unconditionally stable, fourth-order accurate in space, and second-order accurate in time. The optimal pointwise error estimates, unique solvability, and unconditional stability are obtained. Moreover, Richardson extrapolation is exploited to improve the temporal accuracy to fourth order. Finally, numerical results are presented to confirm the theoretical results.
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页数：22
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  • [21] Random attractors for the stochastic coupled fractional Ginzburg-Landau equation with additive noise
    Shu, Ji
    Li, Ping
    Zhang, Jia
    Liao, Ou
    [J]. JOURNAL OF MATHEMATICAL PHYSICS, 2015, 56 (10)
  • [22] Fractional dynamics of coupled oscillators with long-range interaction
    Tarasov, Vasily E.
    Zaslavsky, George M.
    [J]. CHAOS, 2006, 16 (02)
  • [23] Fractional Ginzburg-Landau equation for fractal media
    Tarasov, VE
    Zaslavsky, GM
    [J]. PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2005, 354 : 249 - 261
  • [24] A new technique to solve the initial value problems for fractional fuzzy delay differential equations
    Truong Vinh An
    Ho Vu
    Ngo Van Hoa
    [J]. ADVANCES IN DIFFERENCE EQUATIONS, 2017,
  • [25] Maximum-norm error analysis of a difference scheme for the space fractional CNLS
    Wang, Dongling
    Xiao, Aiguo
    Yang, Wei
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 2015, 257 : 241 - 251
  • [26] Crank-Nicolson difference scheme for the coupled nonlinear Schrodinger equations with the Riesz space fractional derivative
    Wang, Dongling
    Xiao, Aiguo
    Yang, Wei
    [J]. JOURNAL OF COMPUTATIONAL PHYSICS, 2013, 242 : 670 - 681
  • [27] An efficient fourth-order in space difference scheme for the nonlinear fractional Ginzburg-Landau equation
    Wang, Pengde
    Huang, Chengming
    [J]. BIT NUMERICAL MATHEMATICS, 2018, 58 (03) : 783 - 805
  • [28] An implicit midpoint difference scheme for the fractional Ginzburg-Landau equation
    Wang, Pengde
    Huang, Chengming
    [J]. JOURNAL OF COMPUTATIONAL PHYSICS, 2016, 312 : 31 - 49
  • [29] An energy conservative difference scheme for the nonlinear fractional Schrodinger equations
    Wang, Pengde
    Huang, Chengming
    [J]. JOURNAL OF COMPUTATIONAL PHYSICS, 2015, 293 : 238 - 251
  • [30] Analysis of Some Finite Difference Schemes for Two-Dimensional Ginzburg-Landau Equation
    Wang, Tingchun
    Guo, Boling
    [J]. NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2011, 27 (05) : 1340 - 1363
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