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A numerical method for variable‐order fractional version of the coupled 2D Burgers equations by the 2D Chelyshkov polynomials
Author(s) -
Hosseininia M.,
Heydari M. H.,
Maalek Ghaini F. M.
Publication year - 2021
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.7199
Subject(s) - mathematics , discretization , fractional calculus , variable (mathematics) , collocation method , algebraic equation , burgers' equation , order (exchange) , collocation (remote sensing) , algebraic number , mathematical analysis , partial differential equation , nonlinear system , differential equation , computer science , ordinary differential equation , physics , finance , quantum mechanics , machine learning , economics
This paper represents a system of variable‐order (VO) time fractional 2D Burgers equations and expresses a semidiscrete approach by applying the 2D Chelyshkov polynomials (CPs) for solving this system. In this model, the fractional derivative of the Caputo type is considered. To solve this system, we first discretize the VO time fractional derivatives. Next, we obtain a recurrent algorithm by using the weighted finite difference method with parameter θ . Then, utilizing the 2D CPs, we expand the unknown solution and replace it in the main system. In the sequel, we use the differentiation operational matrices and the collocation method to extract an algebraic system of equations which can be easily solved. The validity of the formulated method is investigated through three numerical examples.