TY - JOUR

T1 - Vieta-Lucas polynomials for the coupled nonlinear variable-order fractional Ginzburg-Landau equations

AU - Heydari, M. H.

AU - Avazzadeh, Z.

AU - Razzaghi, M.

N1 - Publisher Copyright:
© 2021 IMACS

PY - 2021/7

Y1 - 2021/7

N2 - In this article, the non-singular variable-order fractional derivative in the Heydari-Hosseininia concept is used to formulate the variable-order fractional form of the coupled nonlinear Ginzburg-Landau equations. To solve this system, a numerical scheme is constructed based upon the shifted Vieta-Lucas polynomials. In this method, with the help of classical and fractional derivative matrices of the shifted Vieta-Lucas polynomials (which are extracted in this study), solving the studied problem is transformed into solving a system of nonlinear algebraic equations. The convergence analysis and the truncation error of the shifted Vieta-Lucas polynomials in two dimensions are investigated. Numerical problems are demonstrated to confirm the convergence rate of the presented algorithm.

AB - In this article, the non-singular variable-order fractional derivative in the Heydari-Hosseininia concept is used to formulate the variable-order fractional form of the coupled nonlinear Ginzburg-Landau equations. To solve this system, a numerical scheme is constructed based upon the shifted Vieta-Lucas polynomials. In this method, with the help of classical and fractional derivative matrices of the shifted Vieta-Lucas polynomials (which are extracted in this study), solving the studied problem is transformed into solving a system of nonlinear algebraic equations. The convergence analysis and the truncation error of the shifted Vieta-Lucas polynomials in two dimensions are investigated. Numerical problems are demonstrated to confirm the convergence rate of the presented algorithm.

KW - Convergence analysis

KW - Coupled nonlinear variable-order fractional Ginzburg-Landau equations

KW - Non-singular variable-order fractional derivative

KW - Vieta-Lucas polynomials

UR - http://www.scopus.com/inward/record.url?scp=85102904557&partnerID=8YFLogxK

U2 - 10.1016/j.apnum.2021.03.007

DO - 10.1016/j.apnum.2021.03.007

M3 - Article

AN - SCOPUS:85102904557

SN - 0168-9274

VL - 165

SP - 442

EP - 458

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

ER -