IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v262y2015icp282-297.html
   My bibliography  Save this article

Efficient numerical techniques for Burgers’ equation

Author

Listed:
  • Mukundan, Vijitha
  • Awasthi, Ashish

Abstract

This paper presents new efficient numerical techniques for solving one dimensional quasi-linear Burgers’ equation. Burgers’ equation is used as a model problem in the study of turbulence, boundary layer behavior, shock waves, convection dominated diffusion phenomena, gas dynamics, acoustic attenuation in fog and continuum traffic simulation. Using a non-linear Cole–Hopf transformation the Burgers’ equation is reduced to one-dimensional diffusion equation. The linearized diffusion equation is semi discretized by using method of lines (MOL) which leads to a system of ordinary differential equations in time. Resulting system of ordinary differential equations is solved by backward differentiation formulas (BDF) of order one, two and three and the analysis of numerical errors are presented. Numerical results for modest values of kinematic viscosity are compared with the exact solution to demonstrate the efficiency of proposed numerical methods.

Suggested Citation

  • Mukundan, Vijitha & Awasthi, Ashish, 2015. "Efficient numerical techniques for Burgers’ equation," Applied Mathematics and Computation, Elsevier, vol. 262(C), pages 282-297.
    • Handle: RePEc:eee:apmaco:v:262:y:2015:i:c:p:282-297
    DOI: 10.1016/j.amc.2015.03.122
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300315004415
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2015.03.122?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.

    Citations

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


    Cited by:

    1. Hassani, Hossein & Naraghirad, Eskandar, 2019. "A new computational method based on optimization scheme for solving variable-order time fractional Burgers’ equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 162(C), pages 1-17.
    2. Guo, Yan & Shi, Yu-feng & Li, Yi-min, 2016. "A fifth-order finite volume weighted compact scheme for solving one-dimensional Burgers’ equation," Applied Mathematics and Computation, Elsevier, vol. 281(C), pages 172-185.
    3. Muaz Seydaoğlu, 2019. "A Meshless Method for Burgers’ Equation Using Multiquadric Radial Basis Functions With a Lie-Group Integrator," Mathematics, MDPI, vol. 7(2), pages 1-11, January.
    4. Chen, Changkai & Zhang, Xiaohua & Liu, Zhang, 2020. "A high-order compact finite difference scheme and precise integration method based on modified Hopf-Cole transformation for numerical simulation of n-dimensional Burgers’ system," Applied Mathematics and Computation, Elsevier, vol. 372(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:262:y:2015:i:c:p:282-297. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.