IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v340y2019icp84-100.html
   My bibliography  Save this article

Compact structure-preserving approach to solitary wave in shallow water modeled by the Rosenau-RLW equation

Author

Listed:
  • Wongsaijai, B.
  • Mouktonglang, T.
  • Sukantamala, N.
  • Poochinapan, K.

Abstract

A mass-preserving scheme, a nonlinear algorithm based on modification of a finite difference method to the Rosenau-RLW equation, is proposed subject to homogeneous boundary conditions. The key feature of the method for improving the accuracy of approximate solutions is to develop a compact higher-order scheme together with an iterative algorithm for solving the nonlinear implicit scheme. The derivatives for space discretization are approximated by using the algorithm dealing with a five-point stencil. In addition, a three-level average difference technique is used to perform time discretization. The conservation of mass and both the existence and uniqueness of the numerical solution are proved. The stability and convergence of the numerical solution with order O(τ4+τ2h2+h4) are also confirmed. For efficiency analysis, numerical results show that the computational efficiency of the compact scheme is much higher than that of non-compact schemes. Moreover, long-time behavior is also used to validate the capability of the present method.

Suggested Citation

  • Wongsaijai, B. & Mouktonglang, T. & Sukantamala, N. & Poochinapan, K., 2019. "Compact structure-preserving approach to solitary wave in shallow water modeled by the Rosenau-RLW equation," Applied Mathematics and Computation, Elsevier, vol. 340(C), pages 84-100.
  • Handle: RePEc:eee:apmaco:v:340:y:2019:i:c:p:84-100
    DOI: 10.1016/j.amc.2018.06.009
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300318304971
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.amc.2018.06.009?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. Mouktonglang, Thanasak & Yimnet, Suriyon & Sukantamala, Nattakorn & Wongsaijai, Ben, 2022. "Dynamical behaviors of the solution to a periodic initial–boundary value problem of the generalized Rosenau-RLW-Burgers equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 196(C), pages 114-136.
    2. Poochinapan, Kanyuta & Wongsaijai, Ben, 2023. "High-performance computing of structure-preserving algorithm for the coupled BBM system formulated by weighted compact difference operators," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 439-467.
    3. Dimitrienko, Yu.I. & Li, Shuguang & Niu, Yi, 2021. "Study on the dynamics of a nonlinear dispersion model in both 1D and 2D based on the fourth-order compact conservative difference scheme," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 661-689.
    4. Wongsaijai, B. & Oonariya, C. & Poochinapan, K., 2020. "Compact structure-preserving algorithm with high accuracy extended to the improved Boussinesq equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 178(C), pages 125-150.
    5. Wongsaijai, Ben & Poochinapan, Kanyuta, 2021. "Optimal decay rates of the dissipative shallow water waves modeled by coupling the Rosenau-RLW equation and the Rosenau-Burgers equation with power of nonlinearity," Applied Mathematics and Computation, Elsevier, vol. 405(C).
    6. Poochinapan, Kanyuta & Wongsaijai, Ben, 2022. "Numerical analysis for solving Allen-Cahn equation in 1D and 2D based on higher-order compact structure-preserving difference scheme," Applied Mathematics and Computation, Elsevier, vol. 434(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:340:y:2019:i:c:p:84-100. 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.