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The Gegenbauer Wavelets-Based Computational Methods for the Coupled System of Burgers’ Equations with Time-Fractional Derivative

Author

Listed:
  • Neslihan Ozdemir

    (Department of Mathematical Engineering, Yildiz Technical University, Istanbul 34220, Turkey)

  • Aydin Secer

    (Department of Mathematical Engineering, Yildiz Technical University, Istanbul 34220, Turkey)

  • Mustafa Bayram

    (Department of Computer Engineering, Gelisim University, Istanbul 34315, Turkey)

Abstract

In this study, Gegenbauer wavelets are used to present two numerical methods for solving the coupled system of Burgers’ equations with a time-fractional derivative. In the presented methods, we combined the operational matrix of fractional integration with the Galerkin method and the collocation method to obtain a numerical solution of the coupled system of Burgers’ equations with a time-fractional derivative. The properties of Gegenbauer wavelets were used to transform this system to a system of nonlinear algebraic equations in the unknown expansion coefficients. The Galerkin method and collocation method were used to find these coefficients. The main aim of this study was to indicate that the Gegenbauer wavelets-based methods is suitable and efficient for the coupled system of Burgers’ equations with time-fractional derivative. The obtained results show the applicability and efficiency of the presented Gegenbaur wavelets-based methods.

Suggested Citation

  • Neslihan Ozdemir & Aydin Secer & Mustafa Bayram, 2019. "The Gegenbauer Wavelets-Based Computational Methods for the Coupled System of Burgers’ Equations with Time-Fractional Derivative," Mathematics, MDPI, vol. 7(6), pages 1-15, May.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:6:p:486-:d:234917
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    References listed on IDEAS

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    1. Singh, Somveer & Patel, Vijay Kumar & Singh, Vineet Kumar, 2018. "Application of wavelet collocation method for hyperbolic partial differential equations via matrices," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 407-424.
    2. Jianping Zhao & Bo Tang & Sunil Kumar & Yanren Hou, 2012. "The Extended Fractional Subequation Method for Nonlinear Fractional Differential Equations," Mathematical Problems in Engineering, Hindawi, vol. 2012, pages 1-11, December.
    3. Prakash, Amit & Kumar, Manoj & Sharma, Kapil K., 2015. "Numerical method for solving fractional coupled Burgers equations," Applied Mathematics and Computation, Elsevier, vol. 260(C), pages 314-320.
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    Cited by:

    1. Manal Alqhtani & Mohamed M. Khader & Khaled Mohammed Saad, 2023. "Numerical Simulation for a High-Dimensional Chaotic Lorenz System Based on Gegenbauer Wavelet Polynomials," Mathematics, MDPI, vol. 11(2), pages 1-12, January.
    2. Shahni, Julee & Singh, Randhir, 2022. "Numerical simulation of Emden–Fowler integral equation with Green’s function type kernel by Gegenbauer-wavelet, Taylor-wavelet and Laguerre-wavelet collocation methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 430-444.

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