IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v358y2019icp394-417.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300319303054
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2019.04.023?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Cavoretto, Roberto, 2022. "Adaptive LOOCV-based kernel methods for solving time-dependent BVPs," Applied Mathematics and Computation, Elsevier, vol. 429(C).
    2. 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).
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yang, Xiaojia & Ge, Yongbin & Lan, Bin, 2021. "A class of compact finite difference schemes for solving the 2D and 3D Burgers’ equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 510-534.
    2. Hammad, D.A. & El-Azab, M.S., 2016. "Chebyshev–Chebyshev spectral collocation method for solving the generalized regularized long wave (GRLW) equation," Applied Mathematics and Computation, Elsevier, vol. 285(C), pages 228-240.
    3. Li, Qi & Mei, Liquan, 2018. "Local momentum-preserving algorithms for the GRLW equation," Applied Mathematics and Computation, Elsevier, vol. 330(C), pages 77-92.
    4. Karakoç, S. Battal Gazi & Zeybek, Halil, 2016. "Solitary-wave solutions of the GRLW equation using septic B-spline collocation method," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 159-171.
    5. Cosgun, Tahir & Sari, Murat, 2020. "Traveling wave solutions and stability behaviours under advection dominance for singularly perturbed advection-diffusion-reaction processes," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:358:y:2019:i:c:p:394-417. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.