IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v36y2008i4p874-882.html
   My bibliography  Save this article

A unified lattice Boltzmann model for some nonlinear partial differential equations

Author

Listed:
  • Chai, Zhenhua
  • Shi, Baochang
  • Zheng, Lin

Abstract

In this paper, a unified and novel lattice Boltzmann model is proposed for solving nonlinear partial differential equation that has the form DUt+αUUx+βUnUx−γUxx+δ Uxxx=F(x,t). Numerical results agree well with the analytical solutions and results derived by existing literature, which indicates the present model is satisfactory and efficient on solving nonlinear partial differential equations.

Suggested Citation

  • Chai, Zhenhua & Shi, Baochang & Zheng, Lin, 2008. "A unified lattice Boltzmann model for some nonlinear partial differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 36(4), pages 874-882.
    • Handle: RePEc:eee:chsofr:v:36:y:2008:i:4:p:874-882
    DOI: 10.1016/j.chaos.2006.07.023
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077906007144
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2006.07.023?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. Helal, M.A. & Mehanna, M.S., 2006. "A comparison between two different methods for solving KdV–Burgers equation," Chaos, Solitons & Fractals, Elsevier, vol. 28(2), pages 320-326.
    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. Lai, Huilin & Ma, Changfeng, 2014. "A new lattice Boltzmann model for solving the coupled viscous Burgers’ equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 395(C), pages 445-457.
    2. Krivovichev, Gerasim V., 2018. "Linear Bhatnagar–Gross–Krook equations for simulation of linear diffusion equation by lattice Boltzmann method," Applied Mathematics and Computation, Elsevier, vol. 325(C), pages 102-119.
    3. Li, Qianhuan & Chai, Zhenhua & Shi, Baochang, 2015. "A novel lattice Boltzmann model for the coupled viscous Burgers’ equations," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 948-957.

    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. Memarbashi, Reza, 2008. "Numerical solution of the Laplace equation in annulus by Adomian decomposition method," Chaos, Solitons & Fractals, Elsevier, vol. 36(1), pages 138-143.
    2. Abdel-Halim Hassan, I.H., 2008. "Comparison differential transformation technique with Adomian decomposition method for linear and nonlinear initial value problems," Chaos, Solitons & Fractals, Elsevier, vol. 36(1), pages 53-65.
    3. Gupta, A.K. & Ray, S. Saha, 2018. "On the solution of time-fractional KdV–Burgers equation using Petrov–Galerkin method for propagation of long wave in shallow water," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 376-380.
    4. Ramos, J.I., 2009. "Generalized decomposition methods for nonlinear oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1078-1084.
    5. Lai, Huilin & Ma, Changfeng, 2009. "Lattice Boltzmann method for the generalized Kuramoto–Sivashinsky equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(8), pages 1405-1412.
    6. Saka, Bülent, 2009. "Cosine expansion-based differential quadrature method for numerical solution of the KdV equation," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2181-2190.

    More about this item

    Statistics

    Access and download statistics

    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:chsofr:v:36:y:2008:i:4:p:874-882. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.