IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v187y2021icp1-16.html
   My bibliography  Save this article

Galerkin approximation with quintic B-spline as basis and weight functions for solving second order coupled nonlinear Schrödinger equations

Author

Listed:
  • Iqbal, Azhar
  • Abd Hamid, Nur Nadiah
  • Md. Ismail, Ahmad Izani
  • Abbas, Muhammad

Abstract

In this article, the Galerkin method, based on quintic B-spline function as the shape and weight functions is described for the numerical solution of the second order coupled nonlinear Schrödinger equations. Finite difference and Crank–Nicolson schemes are used to discretize the time derivative and nodal parameters respectively. Three numerical problems are presented to assess the accuracy and capability of the proposed method. The maximum errors, norms and conserved quantities are calculated. The obtained numerical results show that the present scheme with higher order B-spline as basis and weight functions performs well and accurately. The numerical results are compared with analytical and published results.

Suggested Citation

  • Iqbal, Azhar & Abd Hamid, Nur Nadiah & Md. Ismail, Ahmad Izani & Abbas, Muhammad, 2021. "Galerkin approximation with quintic B-spline as basis and weight functions for solving second order coupled nonlinear Schrödinger equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 1-16.
  • Handle: RePEc:eee:matcom:v:187:y:2021:i:c:p:1-16
    DOI: 10.1016/j.matcom.2021.02.012
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475421000513
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.matcom.2021.02.012?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. Lin, Bin, 2019. "Parametric spline schemes for the coupled nonlinear Schrödinger equation," Applied Mathematics and Computation, Elsevier, vol. 360(C), pages 58-69.
    2. Iqbal, Azhar & Abd Hamid, Nur Nadiah & Md. Ismail, Ahmad Izani, 2020. "Cubic B-spline Galerkin method for numerical solution of the coupled nonlinear Schrödinger equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 174(C), pages 32-44.
    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.

      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:187:y:2021:i:c:p:1-16. 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.