Premium
A numerical method based on the Chebyshev cardinal functions for variable‐order fractional version of the fourth‐order 2D Kuramoto‐Sivashinsky equation
Author(s) -
Hosseininia M.,
Heydari M. H.,
Hooshmandasl M. R.,
Maalek Ghaini F. M.,
Avazzadeh Z.
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6881
Subject(s) - mathematics , chebyshev filter , order (exchange) , algebraic equation , variable (mathematics) , chebyshev polynomials , chebyshev equation , fractional calculus , function (biology) , chebyshev iteration , collocation (remote sensing) , mathematical analysis , nonlinear system , orthogonal polynomials , classical orthogonal polynomials , physics , remote sensing , finance , quantum mechanics , evolutionary biology , economics , biology , geology
In this article, the variable‐order (VO) time fractional 2D Kuramoto‐Sivashinsky equation is introduced, and a semidiscrete approach is presented through 2D Chebyshev cardinal functions (CCFs) for solving this equation. In the proposed method, we obtain a recurrent algorithm by using the finite difference method to approximate the VO fractional differentiation, the weighted finite difference method with parameter θ , and the approximation of the unknown function by the 2D CCFs. The differentiation operational matrices and the collocation technique are used to extract a linear system of algebraic equations which can be easily solved. The credibility of the developed method is examined on three numerical examples.