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Open AccessArticle

Finite Integration Method with Shifted Chebyshev Polynomials for Solving Time-Fractional Burgers’ Equations

1
Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand
2
Department of Mathematics and Statistics, Faculty of Science, Thammasat University, Rangsit Center, Pathum Thani 12120, Thailand
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(12), 1201; https://doi.org/10.3390/math7121201
Received: 21 October 2019 / Revised: 27 November 2019 / Accepted: 3 December 2019 / Published: 7 December 2019
(This article belongs to the Special Issue Numerical Methods)
The Burgers’ equation is one of the nonlinear partial differential equations that has been studied by many researchers, especially, in terms of the fractional derivatives. In this article, the numerical algorithms are invented to obtain the approximate solutions of time-fractional Burgers’ equations both in one and two dimensions as well as time-fractional coupled Burgers’ equations which their fractional derivatives are described in the Caputo sense. These proposed algorithms are constructed by applying the finite integration method combined with the shifted Chebyshev polynomials to deal the spatial discretizations and further using the forward difference quotient to handle the temporal discretizations. Moreover, numerical examples demonstrate the ability of the proposed method to produce the decent approximate solutions in terms of accuracy. The rate of convergence and computational cost for each example are also presented. View Full-Text
Keywords: finite integration method; shifted Chebyshev polynomial; Caputo fractional derivative; Burgers’ equation; coupled Burgers’ equation finite integration method; shifted Chebyshev polynomial; Caputo fractional derivative; Burgers’ equation; coupled Burgers’ equation
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Duangpan, A.; Boonklurb, R.; Treeyaprasert, T. Finite Integration Method with Shifted Chebyshev Polynomials for Solving Time-Fractional Burgers’ Equations. Mathematics 2019, 7, 1201.

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