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A class of high-order compact difference schemes for solving the Burgers’ equations

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  • Yang, Xiaojia
  • Ge, Yongbin
  • Zhang, Lin

Abstract

In this paper, a class of high-order compact difference method is introduced for solving the Burgers’ equations. Firstly, a linear high-order compact difference scheme is proposed to solve the one-dimensional Burgers’ equation. The scheme is fourth-order accurate in space and second-order accurate in time. Linear stability analysis is conducted to show the scheme is conditionally stable. Because only three grid points are involved in each time level, Thomas algorithm can be directly used to solve the tridiagonal linear system. Then, this method is extended to solve the two-dimensional and three-dimensional coupled Burgers’ equations. Numerical experiments are carried out to demonstrate the accuracy and dependability of the present method.

Suggested Citation

  • Yang, Xiaojia & Ge, Yongbin & Zhang, Lin, 2019. "A class of high-order compact difference schemes for solving the Burgers’ equations," Applied Mathematics and Computation, Elsevier, vol. 358(C), pages 394-417.
    • Handle: RePEc:eee:apmaco:v:358:y:2019:i:c:p:394-417
    DOI: 10.1016/j.amc.2019.04.023
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    References listed on IDEAS

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    1. Hammad, D.A. & El-Azab, M.S., 2015. "2N order compact finite difference scheme with collocation method for solving the generalized Burger’s–Huxley and Burger’s–Fisher equations," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 296-311.
    2. Zhanlav, T. & Chuluunbaatar, O. & Ulziibayar, V., 2015. "Higher-order accurate numerical solution of unsteady Burgers’ equation," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 701-707.
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    Cited by:

    1. Korpinar, Zeliha & Inc, Mustafa & Bayram, Mustafa, 2020. "Theory and application for the system of fractional Burger equations with Mittag leffler kernel," Applied Mathematics and Computation, Elsevier, vol. 367(C).
    2. Cavoretto, Roberto, 2022. "Adaptive LOOCV-based kernel methods for solving time-dependent BVPs," Applied Mathematics and Computation, Elsevier, vol. 429(C).
    3. Ying Li & Longxiang Xu & Shihui Ying, 2022. "DWNN: Deep Wavelet Neural Network for Solving Partial Differential Equations," Mathematics, MDPI, vol. 10(12), pages 1-35, June.
    4. Yasir Nawaz & Muhammad Shoaib Arif & Wasfi Shatanawi & Muhammad Usman Ashraf, 2022. "A Fourth Order Numerical Scheme for Unsteady Mixed Convection Boundary Layer Flow: A Comparative Computational Study," Energies, MDPI, vol. 15(3), pages 1-15, January.

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