Alikhanov Legendre—Galerkin Spectral Method for the Coupled Nonlinear Time-Space Fractional Ginzburg–Landau Complex System

Mahmoud A. Zaky, Ahmed S. Hendy and Rob H. De Staelen
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Mahmoud A. Zaky: Department of Applied Mathematics, National Research Centre, Dokki, Cairo 12622, Egypt
Ahmed S. Hendy: Department of Computational Mathematics and Computer Science, Institute of Natural Sciences and Mathematics, Ural Federal University, 19 Mira St., 620002 Yekaterinburg, Russia
Rob H. De Staelen: Dean’s Office of the Faculty of Medicine and Health Sciences, Ghent University, C. Heymanslaan 10, 9000 Gent, Belgium

Mathematics, 2021, vol. 9, issue 2, 1-22

Abstract: A finite difference/Galerkin spectral discretization for the temporal and spatial fractional coupled Ginzburg–Landau system is proposed and analyzed. The Alikhanov L 2 - 1 σ difference formula is utilized to discretize the time Caputo fractional derivative, while the Legendre-Galerkin spectral approximation is used to approximate the Riesz spatial fractional operator. The scheme is shown efficiently applicable with spectral accuracy in space and second-order in time. A discrete form of the fractional Grönwall inequality is applied to establish the error estimates of the approximate solution based on the discrete energy estimates technique. The key aspects of the implementation of the numerical continuation are complemented with some numerical experiments to confirm the theoretical claims.

Keywords: generalized fractional coupled Ginzburg–Landau system; Alikhanov difference formula; Galerkin spectral scheme; discrete fractional Grönwall inequality (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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