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Discrete Chebyshev polynomials for nonsingular variable‐order fractional KdV Burgers' equation
Author(s) -
Heydari Mohammad Hossein,
Avazzadeh Zakieh,
Cattani Carlo
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.6926
Subject(s) - mathematics , invertible matrix , chebyshev polynomials , korteweg–de vries equation , fractional calculus , chebyshev equation , burgers' equation , chebyshev filter , variable (mathematics) , chebyshev nodes , order (exchange) , nonlinear system , mathematical analysis , classical orthogonal polynomials , orthogonal polynomials , pure mathematics , partial differential equation , finance , physics , quantum mechanics , economics
In this article, nonlinear variable‐order (VO) fractional Korteweg‐de Vries (KdV) Burgers' equation with nonsingular VO time fractional derivative is introduced and discussed. The approximate solution of the expressed problem is obtained in the form of a series expansion in terms of the shifted discrete Chebyshev polynomials (CPs) with great accuracy. The method is a computational procedure based on the collocation technique and the shifted discrete CPs together with their operational matrices (ordinary and VO fractional derivatives). The main advantage of the designed approach is that it provides a global solution for the problem. In order to examine the efficiency of the designed algorithm, some numerical problems have been provided. The obtained solutions confirm that the present method is computationally effective and sufficiently accurate in solving this equation.