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Numerical solutions of time and space fractional coupled Burgers equations using time–space Chebyshev pseudospectral method
Author(s) -
Mittal Avinash K.,
Balyan Lokendra K.
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.6592
Subject(s) - mathematics , fractional calculus , chebyshev pseudospectral method , mathematical analysis , burgers' equation , nonlinear system , chebyshev equation , algebraic equation , chebyshev filter , space (punctuation) , partial differential equation , classical orthogonal polynomials , physics , quantum mechanics , orthogonal polynomials , linguistics , philosophy
The aim of the paper is to develop and analyze a spectrally accurate time–space pseudospectral method to the approximate solution of nonlinear time and space fractional coupled Burgers equations. Liouville–Caputo fractional derivative formula is used to evaluate the fractional derivatives matrix at CGL points. Using the Chebyshev fractional derivative matrices, the given problem is reduced to a system of nonlinear algebraic equations. A mapping is used to transform the nonhomogeneous initial–boundary values to homogeneous initial–boundary values. Error analysis of the proposed method for the equation is presented. A model example of fractional coupled Burgers equations is tested for a set of fractional‐order derivatives. For the proposed method, highly accurate numerical results are obtained, which confirm the accuracy and efficiency of the proposed method.