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Compact operator method of accuracy two in time and four in space for the numerical solution of coupled viscous Burgers’ equations

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  • Mohanty, R.K.
  • Dai, Weizhong
  • Han, Fei

Abstract

In this paper, we propose a new two-level implicit compact operator method of order two in time (t) and four in space (x) for the solution of time dependent coupled viscous Burgers’ equations. In this method, we did not use any transformation or linearization technique to handle nonlinearity. We use only 3-spatial grid points and the obtained tridiagonal nonlinear system has been solved by Newton’s iterative method. The test problems considered in the literature have been discussed to demonstrate the strength and utility of the proposed method. The computed numerical solutions are in good agreement with the exact solutions and competent with those available in earlier studies. We show that the proposed method enables us to obtain high accurate solution for high Reynolds number.

Suggested Citation

  • Mohanty, R.K. & Dai, Weizhong & Han, Fei, 2015. "Compact operator method of accuracy two in time and four in space for the numerical solution of coupled viscous Burgers’ equations," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 381-393.
    • Handle: RePEc:eee:apmaco:v:256:y:2015:i:c:p:381-393
    DOI: 10.1016/j.amc.2015.01.051
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    References listed on IDEAS

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    1. 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. Başhan, Ali, 2020. "A numerical treatment of the coupled viscous Burgers’ equation in the presence of very large Reynolds number," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    2. Park, Sangbeom & Kim, Philsu & Jeon, Yonghyeon & Bak, Soyoon, 2022. "An economical robust algorithm for solving 1D coupled Burgers’ equations in a semi-Lagrangian framework," Applied Mathematics and Computation, Elsevier, vol. 428(C).

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