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A Jacobi collocation approximation for nonlinear coupled viscous Burgers’ equation

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Central European Journal of Physics

Abstract

This article presents a numerical approximation of the initial-boundary nonlinear coupled viscous Burgers’ equation based on spectral methods. A Jacobi-Gauss-Lobatto collocation (J-GL-C) scheme in combination with the implicit Runge-Kutta-Nyström (IRKN) scheme are employed to obtain highly accurate approximations to the mentioned problem. This J-GL-C method, based on Jacobi polynomials and Gauss-Lobatto quadrature integration, reduces solving the nonlinear coupled viscous Burgers’ equation to a system of nonlinear ordinary differential equation which is far easier to solve. The given examples show, by selecting relatively few J-GL-C points, the accuracy of the approximations and the utility of the approach over other analytical or numerical methods. The illustrative examples demonstrate the accuracy, efficiency, and versatility of the proposed algorithm.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt

    Eid H. Doha

  2. Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia

    Ali H. Bhrawy

  3. Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt

    Ali H. Bhrawy & Mohamed A. Abdelkawy

  4. Department of Basic Science, Institute of Information Technology, Modern Academy, Cairo, Egypt

    Ramy M. Hafez

Authors
  1. Eid H. Doha
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  2. Ali H. Bhrawy
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  3. Mohamed A. Abdelkawy
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  4. Ramy M. Hafez
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Corresponding author

Correspondence to Mohamed A. Abdelkawy.

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Doha, E.H., Bhrawy, A.H., Abdelkawy, M.A. et al. A Jacobi collocation approximation for nonlinear coupled viscous Burgers’ equation. centr.eur.j.phys. 12, 111–122 (2014). https://doi.org/10.2478/s11534-014-0429-z

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  • DOI: https://doi.org/10.2478/s11534-014-0429-z

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