An efficient difference scheme for the coupled nonlinear fractional Ginzburg–Landau equations with the fractional Laplacian
Numerical Methods for Partial Differential Equations2018Vol. 35(1), pp. 394–421
Citations Over TimeTop 10% of 2018 papers
Abstract
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 Grünwald difference method in space. Then, we prove that the scheme is uniquely solvable, and the numerical solutions are bounded and unconditionally convergent in the norm. Finally, numerical tests are given to confirm the theoretical results and show the effectiveness of the scheme.
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