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A new computational method based on optimization scheme for solving variable-order time fractional Burgers’ equation

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  • Hassani, Hossein
  • Naraghirad, Eskandar

Abstract

In this paper, an optimization method based on the generalized polynomials (GPs) as the basis functions is proposed for solving the variable-order time fractional Burgers’ equation (V-TFBE). In this method, the solution is considered as an GPs with unknown free coefficients and control parameters. The primary purpose of this paper is to employ a new variable-order operational matrix for GPs in the Caputo sense. Then we use the Lagrange multipliers technique for converting the problem under study into a system of nonlinear algebraic equations with unknown free coefficients and control parameters which constructs an approximate solution for the problem under study. The convergence analysis is guaranteed by obtaining a new result concerning the functions of two variables. The efficiency of the proposed method is illustrated by three numerical experiments, which confirm that obtained results are in good agreement with the exact solution.

Suggested Citation

  • Hassani, Hossein & Naraghirad, Eskandar, 2019. "A new computational method based on optimization scheme for solving variable-order time fractional Burgers’ equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 162(C), pages 1-17.
    • Handle: RePEc:eee:matcom:v:162:y:2019:i:c:p:1-17
    DOI: 10.1016/j.matcom.2019.01.002
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    References listed on IDEAS

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    1. Mukundan, Vijitha & Awasthi, Ashish, 2015. "Efficient numerical techniques for Burgers’ equation," Applied Mathematics and Computation, Elsevier, vol. 262(C), pages 282-297.
    2. Zhou, Fengying & Xu, Xiaoyong, 2016. "The third kind Chebyshev wavelets collocation method for solving the time-fractional convection diffusion equations with variable coefficients," Applied Mathematics and Computation, Elsevier, vol. 280(C), pages 11-29.
    3. Tamsir, Mohammad & Srivastava, Vineet K. & Jiwari, Ram, 2016. "An algorithm based on exponential modified cubic B-spline differential quadrature method for nonlinear Burgers’ equation," Applied Mathematics and Computation, Elsevier, vol. 290(C), pages 111-124.
    4. Yang, Xiao-Jun & Machado, J.A. Tenreiro, 2017. "A new fractional operator of variable order: Application in the description of anomalous diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 481(C), pages 276-283.
    5. Carillo, Sandra & Lo Schiavo, Mauro & Schiebold, Cornelia, 2018. "Recursion operators admitted by non-Abelian Burgers equations: Some remarks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 147(C), pages 40-51.
    6. Soliman, A.A., 2006. "The modified extended tanh-function method for solving Burgers-type equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 361(2), pages 394-404.
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    Cited by:

    1. Heydari, M.H., 2020. "Chebyshev cardinal functions for a new class of nonlinear optimal control problems generated by Atangana–Baleanu–Caputo variable-order fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    2. Peng, Xiangyi & Xu, Da & Qiu, Wenlin, 2023. "Pointwise error estimates of compact difference scheme for mixed-type time-fractional Burgers’ equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 702-726.

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