We found a match
Your institution may have rights to this item. Sign in to continue.
- Title
Alikhanov Legendre—Galerkin Spectral Method for the Coupled Nonlinear Time-Space Fractional Ginzburg–Landau Complex System.
- Authors
Zaky, Mahmoud A.; Hendy, Ahmed S.; De Staelen, Rob H.
- 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.
- Subjects
GALERKIN methods; CAPUTO fractional derivatives; ESTIMATION theory; FINITE differences
- Publication
Mathematics (2227-7390), 2021, Vol 9, Issue 2, p183
- ISSN
2227-7390
- Publication type
Article
- DOI
10.3390/math9020183