https://doi.org/10.1140/epjs/s11734-023-00921-6
Regular Article
Stability analysis and error estimates of local discontinuous Galerkin method for nonlinear fractional Ginzburg–Landau equation with the fractional Laplacian
1
Department of Mathematics, Unaizah College of Sciences and Arts, Qassim University, Qassim, Saudi Arabia
2
Department of Mathematics, College of Science and Arts, Qassim University, Ar Rass, Saudi Arabia
3
Department of Mathematics, Assiut University, 71516, Assiut, Egypt
a T.aboelenen@qu.edu.sa, tarek.aboelenen@aun.edu.eg
Received:
22
March
2023
Accepted:
2
July
2023
Published online:
27
July
2023
In this paper, we present and analyze local discontinuous Galerkin (LDG) method to solve nonlinear fractional Ginzburg–Landau equation (FGLE) with the fractional Laplacian. This method transforms the nonlinear FGLE with fractional Laplacian of order 
into a system of first-order equations and approximates the solution of the equation by selecting the appropriate basis functions. The stability analysis for FGLE has been investigated, and the optimal convergence rates 
of the semi-discrete scheme have been established. Finally, numerical examples are displayed to verify the theoretical results.
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
