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.

引用

页数：22

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