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

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...

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Bibliographic Details
Published in:Mathematics (Basel) Vol. 7; no. 12; p. 1201
Main Authors: Duangpan, Ampol, Boonklurb, Ratinan, Treeyaprasert, Tawikan
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.12.2019
Subjects:
Algorithms
Applied mathematics
Approximation
Burgers equation
Calculus
Chebyshev approximation
Finite volume method
Integral equations
Mathematical functions
Mathematical models
Mathematics
Nonlinear differential equations
Numerical analysis
Partial differential equations
Polynomials
Quotients
ISSN:2227-7390, 2227-7390
Online Access:Get full text
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Summary: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.
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ISSN:2227-7390
2227-7390
DOI:10.3390/math7121201