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Matrix method based on the shifted Chebyshev polynomials for solving fractional‐order PDEs with initial‐boundary conditions
Author(s) -
Zhao Fuqiang,
Huang Qingxue,
Xie Jiaquan,
Ma Lifeng
Publication year - 2018
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.4438
Subject(s) - mathematics , chebyshev polynomials , chebyshev filter , algebraic equation , chebyshev equation , boundary value problem , order (exchange) , matrix (chemical analysis) , chebyshev iteration , algebraic number , boundary (topology) , mathematical analysis , orthogonal polynomials , classical orthogonal polynomials , nonlinear system , physics , materials science , finance , quantum mechanics , economics , composite material
In the current study, we consider the approximate solutions of fractional‐order PDEs with initial‐boundary conditions based on the shifted Chebyshev polynomials. The proposed method is combined with the operational matrix of fractional‐order differentiation described in the Caputo's sense. The main characteristic behind this approach is to reduce such problems to those of solving systems of algebraic equations with constant coefficients by dispersing unknown variables. The validity and effectiveness of the approach are demonstrated via some numerical examples. Lastly, the error analysis of the proposed method has been investigated. Copyright © 2017 John Wiley & Sons, Ltd.