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...

Celý popis

Uloženo v:
Podrobná bibliografie
Vydáno v:Mathematics (Basel) Ročník 7; číslo 12; s. 1201
Hlavní autoři: Duangpan, Ampol, Boonklurb, Ratinan, Treeyaprasert, Tawikan
Médium: Journal Article
Jazyk:angličtina
Vydáno: Basel MDPI AG 01.12.2019
Témata:
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
On-line přístup:Získat plný text
Tagy: Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
Popis
Shrnutí: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.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:2227-7390
2227-7390
DOI:10.3390/math7121201