An efficient difference scheme for the coupled nonlinear fractional Ginzburg-Landau equations with the fractional Laplacian

作者：Li, Meng; Huang, Chengming^*

来源：Numerical Methods for Partial Differential Equations, 2019, 35(1): 394-421.

DOI：10.1002/num.22305

• convergence
• coupled fractional Ginzburg-Landau equations
• fractional Laplacian
• implicit midpoint scheme
• Riesz fractional derivative
• weighted and shifted Grunwald difference

In this article, an efficient difference scheme for the coupled fractional Ginzburg-Landau equations with the fractional Laplacian is studied. We construct the discrete scheme based on the implicit midpoint method in time and a weighted and shifted Grunwald difference method in space. Then, we prove that the scheme is uniquely solvable, and the numerical solutions are bounded and unconditionally convergent in the lh2 norm. Finally, numerical tests are given to confirm the theoretical results and show the effectiveness of the scheme.

• 出版日期2019-1
• 单位华中科技大学; 郑州大学