Paper Info
Title
Chebyshev Polynomials For The Numerical Solution Of Fractal-Fractional Model Of Nonlinear Ginzburg-Landau Equation
Abstract
This paper introduces a new version for the nonlinear Ginzburg-Landau equation derived from fractal-fractional derivatives and proposes a computational scheme for their numerical solutions. The fractal-fractional derivative is defined in the Atangana-Riemann-Liouville sense with Mittage-Leffler kernel. The proposed approach is based on the shifted Chebyshev polynomials (S-CPs) and the collocation scheme. Through the way, a new operational matrix (OM) of fractal-fractional derivative is derived for the S-CPs and used in the presented method. More precisely, the unknown solution is separated into their real and imaginary parts, and then, these parts are expanded in terms of the S-CPs with undetermined coefficients. These expansions are substituted into the main equation and the generated operational matrix is utilized to extract a system of nonlinear algebraic equations. Thereafter, the yielded system is solved to obtain the approximate solution of the problem. The accuracy of the proposed approach is examined through some numerical examples. Numerical results confirm the suggested approach is very accurate to provide satisfactory results.
Year
DOI
Venue
2021
10.1007/s00366-019-00889-9
ENGINEERING WITH COMPUTERS
Keywords
DocType
Volume
Fractal-fractional Ginzburg-Landau equation, Shifted Chebyshev polynomials (SCPs), Operational matrix (OM), OM of fractal-fractional derivative
Journal
37
Issue
ISSN
Citations 
2
0177-0667
2
PageRank 
References 
Authors
0.42
0
3
Name
Order
Citations
PageRank
M. H. Heydari162.99
Abdon Atangana27112.66
Zakieh Avazzadeh3135.90