IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v207y2023icp226-242.html
   My bibliography  Save this article

Petrov–Galerkin approximation of time-fractional coupled Korteweg–de Vries equation for propagation of long wave in shallow water

Author

Listed:
  • Arifeen, Shams Ul
  • Haq, Sirajul

Abstract

The time-fractional coupled Korteweg–de Vries equations (TFCKdVEs) describe various interesting real-world phenomena including wave propagation and the description of shallow water waves on a viscous fluid. This paper presents an accurate and robust numerical technique to solve the TFCKdVE. The cubic B-spline is introduced as a basis function and a quadratic B-spline is used as a test function in a finite element method (FEM) is known as Petrov–Galerkin method. The temporal fractional part is simplified via L1 formula, while the B-spline is employed for the space approximation. The Lax–Richtmyer stability criterion is applied to analyze the stability of the proposed scheme. Four test problems are solved to check performance and validation of the scheme. The accuracy and efficiency of the proposed method are checked via various error norms. The obtained results show good agreement with the exact solutions and earlier work available in the literature.

Suggested Citation

  • Arifeen, Shams Ul & Haq, Sirajul, 2023. "Petrov–Galerkin approximation of time-fractional coupled Korteweg–de Vries equation for propagation of long wave in shallow water," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 226-242.
    • Handle: RePEc:eee:matcom:v:207:y:2023:i:c:p:226-242
    DOI: 10.1016/j.matcom.2022.12.028
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475422005158
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2022.12.028?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. Abdon Atangana & Aydin Secer, 2013. "The Time-Fractional Coupled-Korteweg-de-Vries Equations," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, March.
    2. Helal, M.A. & El-Eissa, H.N., 1996. "Shallow water waves and Korteweg-de Vries equation (oceanographical application)," Pure Mathematics and Applications, Department of Mathematics, Corvinus University of Budapest, vol. 7(3-4), pages 263-282.
    3. Noufe H. Aljahdaly & Ali Akgül & Rasool Shah & Ibrahim Mahariq & Jeevan Kafle & A. Ghareeb, 2022. "A Comparative Analysis of the Fractional-Order Coupled Korteweg–De Vries Equations with the Mittag–Leffler Law," Journal of Mathematics, Hindawi, vol. 2022, pages 1-30, February.
    4. Hussain, Manzoor & Haq, Sirajul & Ghafoor, Abdul, 2019. "Meshless spectral method for solution of time-fractional coupled KdV equations," Applied Mathematics and Computation, Elsevier, vol. 341(C), pages 321-334.
    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. Owyed, Saud & Abdou, M.A. & Abdel-Aty, Abdel-Haleem & Alharbi, W. & Nekhili, Ramzi, 2020. "Numerical and approximate solutions for coupled time fractional nonlinear evolutions equations via reduced differential transform method," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    2. Agarwal, P. & Deni̇z, S. & Jain, S. & Alderremy, A.A. & Aly, Shaban, 2020. "A new analysis of a partial differential equation arising in biology and population genetics via semi analytical techniques," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 542(C).
    3. M. Mossa Al-Sawalha & Ravi P. Agarwal & Rasool Shah & Osama Y. Ababneh & Wajaree Weera, 2022. "A Reliable Way to Deal with Fractional-Order Equations That Describe the Unsteady Flow of a Polytropic Gas," Mathematics, MDPI, vol. 10(13), pages 1-13, June.
    4. Liang, Hejun & Pirouzi, Sasan, 2024. "Energy management system based on economic Flexi-reliable operation for the smart distribution network including integrated energy system of hydrogen storage and renewable sources," Energy, Elsevier, vol. 293(C).
    5. Lei Fu & Yaodeng Chen & Hongwei Yang, 2019. "Time-Space Fractional Coupled Generalized Zakharov-Kuznetsov Equations Set for Rossby Solitary Waves in Two-Layer Fluids," Mathematics, MDPI, vol. 7(1), pages 1-13, January.
    6. Hussain, Manzoor & Haq, Sirajul & Ghafoor, Abdul, 2019. "Meshless spectral method for solution of time-fractional coupled KdV equations," Applied Mathematics and Computation, Elsevier, vol. 341(C), pages 321-334.
    7. Helal, M.A. & Mehanna, M.S., 2008. "Tsunamis from nature to physics," Chaos, Solitons & Fractals, Elsevier, vol. 36(4), pages 787-796.

    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:207:y:2023:i:c:p:226-242. 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.