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

Author

Listed:
  • Ampol Duangpan

    (Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand)

  • Ratinan Boonklurb

    (Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand)

  • Tawikan Treeyaprasert

    (Department of Mathematics and Statistics, Faculty of Science, Thammasat University, Rangsit Center, Pathum Thani 12120, Thailand)

Abstract

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.

Suggested Citation

  • Ampol Duangpan & Ratinan Boonklurb & Tawikan Treeyaprasert, 2019. "Finite Integration Method with Shifted Chebyshev Polynomials for Solving Time-Fractional Burgers’ Equations," Mathematics, MDPI, vol. 7(12), pages 1-24, December.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:12:p:1201-:d:295445
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    References listed on IDEAS

    as
    1. Yun, D.F. & Wen, Z.H. & Hon, Y.C., 2015. "Adaptive least squares finite integration method for higher-dimensional singular perturbation problems with multiple boundary layers," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 232-250.
    2. Huamin Zhang & Feng Ding, 2013. "On the Kronecker Products and Their Applications," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-8, June.
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    Cited by:

    1. Waleed Mohamed Abd-Elhameed, 2022. "Novel Formulae of Certain Generalized Jacobi Polynomials," Mathematics, MDPI, vol. 10(22), pages 1-25, November.

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