文献类型：期刊文献

英文题名：An efficient fourth-order in space difference scheme for the nonlinear fractional Ginzburg-Landau equation

作者：Wang, Pengde[1];Huang, Chengming[2,3]

第一作者：Wang, Pengde

通讯作者：Huang, CM[1];Huang, CM[2]

机构：[1]Henan Univ Econ & Law, Coll Math & Informat Sci, Zhengzhou 450000, Henan, Peoples R China;[2]Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Hubei, Peoples R China;[3]Huazhong Univ Sci & Technol, Hubei Key Lab Engn Modeling & Sci Comp, Wuhan 430074, Hubei, Peoples R China

第一机构：河南财经政法大学数学与信息科学学院

通讯机构：[1]corresponding author), Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Hubei, Peoples R China;[2]corresponding author), Huazhong Univ Sci & Technol, Hubei Key Lab Engn Modeling & Sci Comp, Wuhan 430074, Hubei, Peoples R China.

年份：2018

卷号：58

期号：3

起止页码：783-805

外文期刊名：BIT NUMERICAL MATHEMATICS

收录：;Scopus(收录号：2-s2.0-85042124603);WOS:【SCI-EXPANDED(收录号:WOS:000444946100011)】；

基金：This work was supported by National Natural Science Foundation of China (No. 11771163).

语种：英文

外文关键词：Fractional Ginzburg-Landau equation; Riesz fractional derivative; Implicit-explicit method; Fractional compact scheme; Convergence

摘要：This paper proposes and analyzes a high-order implicit-explicit difference scheme for the nonlinear complex fractional Ginzburg-Landau equation involving the Riesz fractional derivative. For the time discretization, the second-order backward differentiation formula combined with the explicit second-order Gear's extrapolation is adopted. While for the space discretization, a fourth-order fractional quasi-compact method is used to approximate the Riesz fractional derivative. The scheme is efficient in the sense that, at each time step, only a linear system with a coefficient matrix independent of the time level needs to be solved. Despite of the explicit treatment of the nonlinear term, the scheme is shown to be unconditionally convergent in the l2 h norm, semi-H-h(alpha/2) norm and l(h)(infinity) norm at the order of O(tau(2) + h(4)) with tau time step and h mesh size. Numerical tests are provided to confirm the accuracy and efficiency of the scheme.