IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v194y2022icp169-184.html
   My bibliography  Save this article

Numerical approximation of modified Kawahara equation using Kernel smoothing method

Author

Listed:
  • Zara, Aiman
  • Rehman, Shafiq Ur
  • Ahmad, Fayyaz
  • Kouser, Salima
  • Pervaiz, Anjum

Abstract

In this article, a numerical approximation of modified Kawahara equation is investigated by Kernel smoothing method. The spatial derivatives involved in the modified Kawahara equation are approximated by smoothing Kernel method. Whereas, for the time integration, we employ Crank–Nicolson method. The conservative nature of the proposed scheme is demonstrated by the mass conservation constant (I1) and energy conservation constant (I2). To quantify the quality of the proposed scheme, we also have performed numerical testing on a collection of test problems.

Suggested Citation

  • Zara, Aiman & Rehman, Shafiq Ur & Ahmad, Fayyaz & Kouser, Salima & Pervaiz, Anjum, 2022. "Numerical approximation of modified Kawahara equation using Kernel smoothing method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 169-184.
    • Handle: RePEc:eee:matcom:v:194:y:2022:i:c:p:169-184
    DOI: 10.1016/j.matcom.2021.11.014
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475421004109
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2021.11.014?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. Nur Hasan Mahmud Shahen & Foyjonnesa & Md Habibul Bashar & Tasnim Tahseen & Sakhawat Hossain, 2021. "Solitary and Rogue Wave Solutions to the Conformable Time Fractional Modified Kawahara Equation in Mathematical Physics," Advances in Mathematical Physics, Hindawi, vol. 2021, pages 1-9, July.
    2. Zehra Pınar & Turgut Öziş, 2013. "The Periodic Solutions to Kawahara Equation by Means of the Auxiliary Equation with a Sixth-Degree Nonlinear Term," Journal of Mathematics, Hindawi, vol. 2013, pages 1-8, March.
    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. Ahmad, Fayyaz & Ur Rehman, Shafiq & Zara, Aiman, 2023. "A new approach for the numerical approximation of modified Korteweg–de Vries equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 189-206.

    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. Peiyao Wang & Shangwen Peng & Yihao Cao & Rongpei Zhang, 2024. "The Conservative and Efficient Numerical Method of 2-D and 3-D Fractional Nonlinear Schrödinger Equation Using Fast Cosine Transform," Mathematics, MDPI, vol. 12(7), pages 1-14, April.
    2. El-Tantawy, S.A. & Salas, Alvaro H. & Alharthi, M.R., 2021. "Novel analytical cnoidal and solitary wave solutions of the Extended Kawahara equation," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    3. Ahmad, Fayyaz & Ur Rehman, Shafiq & Zara, Aiman, 2023. "A new approach for the numerical approximation of modified Korteweg–de Vries equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 189-206.
    4. Hamood Ur Rehman & Ifrah Iqbal & Suhad Subhi Aiadi & Nabil Mlaiki & Muhammad Shoaib Saleem, 2022. "Soliton Solutions of Klein–Fock–Gordon Equation Using Sardar Subequation Method," Mathematics, MDPI, vol. 10(18), pages 1-10, September.
    5. Kaltham K. Al-Kalbani & Khalil S. Al-Ghafri & Edamana V. Krishnan & Anjan Biswas, 2023. "Optical Solitons and Modulation Instability Analysis with Lakshmanan–Porsezian–Daniel Model Having Parabolic Law of Self-Phase Modulation," Mathematics, MDPI, vol. 11(11), pages 1-20, May.

    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:194:y:2022:i:c:p:169-184. 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.