Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/103130
Title: Alikhanov Legendre—Galerkin spectral method for the coupled nonlinear time-space fractional Ginzburg–Landau complex system
Authors: Zaky, M. A.
Hendy, A. S.
De Staelen, R. H.
Issue Date: 2021
Publisher: MDPI AG
Citation: Zaky M. A. Alikhanov Legendre—Galerkin spectral method for the coupled nonlinear time-space fractional Ginzburg–Landau complex system / M. A. Zaky, A. S. Hendy, R. H. De Staelen. — DOI 10.3390/math9020183 // Mathematics. — 2021. — Vol. 9. — Iss. 2. — P. 1-22. — 183.
Abstract: A finite difference/Galerkin spectral discretization for the temporal and spatial fractional coupled Ginzburg–Landau system is proposed and analyzed. The Alikhanov L2-1σ 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. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.
Keywords: ALIKHANOV DIFFERENCE FORMULA
DISCRETE FRACTIONAL GRÖNWALL INEQUALITY
GALERKIN SPECTRAL SCHEME
GENERALIZED FRACTIONAL COUPLED GINZBURG–LANDAU SYSTEM
URI: http://hdl.handle.net/10995/103130
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 85099937927
PURE ID: 20894297
87449e94-ceaa-44d0-a8c4-233afc613747
ISSN: 22277390
DOI: 10.3390/math9020183
metadata.dc.description.sponsorship: The first author wishes to acknowledge the financial support of the National Research Centre of Egypt (NRC). The second author wishes to acknowledge the support of RFBR Grant 19-01-00019.
Appears in Collections:Научные публикации, проиндексированные в SCOPUS и WoS CC

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