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Novel operational matrices-based finite difference/spectral algorithm for a class of time-fractional Burger equation in multidimensions

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  • Usman, Muhammad
  • Hamid, Muhammad
  • Liu, Moubin

Abstract

In this work, an innovative computational scheme is developed to compute stable solutions of time-fractional coupled viscous Burger's equation in multi-dimensions. To discretize the problem, the temporal derivative is approximated through a forward difference scheme whereas the spatial derivatives are approximated assisted by novel operational matrices that have been constructed via shifted Gegenbauer wavelets (SGWs). The piecewise functions are utilized to construct the operational matrices of multi-dimensional SGWs vectors although related theorems are offered to authenticate the scheme mathematically. The proposed computational algorithm converts the model understudy to a system of linear algebraic equations that are easier to tackle. To validate the accuracy, credibility, and reliability of the present method, the time-fractional viscous Burger's models are considered in one, two, and three dimensions. An inclusive comparative study is reported which demonstrates that the proposed computational scheme is effective, accurate, and well-matched to find the numerical solutions of the aforementioned problems. Convergence, error bound, and stability of the suggested method is investigated theoretically and numerically.

Suggested Citation

  • Usman, Muhammad & Hamid, Muhammad & Liu, Moubin, 2021. "Novel operational matrices-based finite difference/spectral algorithm for a class of time-fractional Burger equation in multidimensions," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    • Handle: RePEc:eee:chsofr:v:144:y:2021:i:c:s0960077921000540
    DOI: 10.1016/j.chaos.2021.110701
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    References listed on IDEAS

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    1. Ray, S. Saha & Gupta, A.K., 2015. "A numerical investigation of time-fractional modified Fornberg–Whitham equation for analyzing the behavior of water waves," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 135-148.
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    4. Hsiao, Chun-Hui & Wang, Wen-June, 2001. "Haar wavelet approach to nonlinear stiff systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 57(6), pages 347-353.
    5. Usman, M. & Hamid, M. & Zubair, T. & Haq, R.U. & Wang, W. & Liu, M.B., 2020. "Novel operational matrices-based method for solving fractional-order delay differential equations via shifted Gegenbauer polynomials," Applied Mathematics and Computation, Elsevier, vol. 372(C).
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    Cited by:

    1. Cao, Baiheng & Wu, Xuedong & Wang, Yaonan & Zhu, Zhiyu, 2024. "Modified hybrid B-spline estimation based on spatial regulator tensor network for burger equation with nonlinear fractional calculus," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 220(C), pages 253-275.
    2. Hamid, Muhammad & Usman, Muhammad & Yan, Yaping & Tian, Zhenfu, 2022. "An efficient numerical scheme for fractional characterization of MHD fluid model," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    3. Hamid, Muhammad & Usman, Muhammad & Yan, Yaping & Tian, Zhenfu, 2023. "A computational numerical algorithm for thermal characterization of fractional unsteady free convection flow in an open cavity," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).

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