IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v204y2023icp216-229.html
   My bibliography  Save this article

Direct WENO scheme for dispersion-type equations

Author

Listed:
  • Ahmat, Muyassar
  • Qiu, Jianxian

Abstract

In this paper, we present a weighted essentially non-oscillatory (WENO) scheme for dispersive equations which may generate physical high-frequency oscillation in the non-smooth interface. The third derivative term is approximated directly by a conservative flux difference. A finite-difference WENO scheme of fifth-order is constructed for the discretization of spatial differentiation. The wave behavior of linear and nonlinear dispersion equations is simulated by using the proposed scheme in space direction and the third-order TVD Runge–Kutta method in the time direction. Numerical examples demonstrate the accuracy and good performance of the proposed scheme.

Suggested Citation

  • Ahmat, Muyassar & Qiu, Jianxian, 2023. "Direct WENO scheme for dispersion-type equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 216-229.
  • Handle: RePEc:eee:matcom:v:204:y:2023:i:c:p:216-229
    DOI: 10.1016/j.matcom.2022.08.010
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475422003561
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.matcom.2022.08.010?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. Ismail, M.S. & Taha, T.R., 1998. "A numerical study of compactons," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 47(6), pages 519-530.
    2. Rathan, Samala & Kumar, Rakesh & Jagtap, Ameya D., 2020. "L1-type smoothness indicators based WENO scheme for nonlinear degenerate parabolic equations," Applied Mathematics and Computation, Elsevier, vol. 375(C).
    Full references (including those not matched with items on IDEAS)

    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. Wazwaz, A.M., 2001. "A study of nonlinear dispersive equations with solitary-wave solutions having compact support," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 56(3), pages 269-276.
    2. Odibat, Zaid M., 2009. "Exact solitary solutions for variants of the KdV equations with fractional time derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1264-1270.
    3. Rus, Francisco & Villatoro, Francisco R., 2007. "Padé numerical method for the Rosenau–Hyman compacton equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 76(1), pages 188-192.
    4. Yin, Jun & Lai, Shaoyong & Qing, Yin, 2009. "Exact solutions to a nonlinear dispersive model with variable coefficients," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1249-1254.
    5. Wazwaz, Abdul-Majid, 2005. "Generalized forms of the phi-four equation with compactons, solitons and periodic solutions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 69(5), pages 580-588.
    6. Chen, Yong & Li, Biao & Zhang, Hongqing, 2004. "New exact solutions for modified nonlinear dispersive equations mK(m,n) in higher dimensions spaces," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 64(5), pages 549-559.
    7. Wazwaz, A.M., 2002. "General compactons solutions and solitary patterns solutions for modified nonlinear dispersive equations mK(n,n) in higher dimensional spaces," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 59(6), pages 519-531.
    8. Kuru, S., 2009. "Compactons and kink-like solutions of BBM-like equations by means of factorization," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 626-633.
    9. Xu, Chuanhai & Tian, Lixin, 2009. "The bifurcation and peakon for K(2,2) equation with osmosis dispersion," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 893-901.
    10. Garralon-López, Rubén & Rus, Francisco & Villatoro, Francisco R., 2023. "Robustness of the absolute Rosenau–Hyman |K|(p,p) equation with non-integer p," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    11. Wazwaz, Abdul-Majid & Taha, Thiab, 2003. "Compact and noncompact structures in a class of nonlinearly dispersive equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 62(1), pages 171-189.
    12. Yadong, Shang, 2005. "Explicit and exact special solutions for BBM-like B(m,n) equations with fully nonlinear dispersion," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 1083-1091.
    13. Wazwaz, Abdul-Majid, 2003. "An analytic study of compactons structures in a class of nonlinear dispersive equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 63(1), pages 35-44.

    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:matcom:v:204:y:2023:i:c:p:216-229. 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: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.