IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v174y2020icp32-44.html
   My bibliography  Save this article

Cubic B-spline Galerkin method for numerical solution of the coupled nonlinear Schrödinger equation

Author

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

Abstract

In this paper, the Galerkin method, based on cubic B-spline function as the shape and weight functions is applied for the numerical solution of the one-dimensional coupled nonlinear Schrödinger equation. Numerical experiments involving single solitary wave, collision of two solitary waves and collision of three solitary waves are conducted. The obtained numerical results of the proposed scheme are compared with the analytical results and previously published numerical results. Two conserved quantities I1 and I2 are calculated for collision of two solitary waves and interaction of three solitary waves. The scheme provides accurate results which are in good agreement when compared to other numerical schemes. The order of convergence of the scheme is calculated. Moreover, the use of cubic B-spline Galerkin method produces smooth solutions without numerical smearing.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:174:y:2020:i:c:p:32-44
    DOI: 10.1016/j.matcom.2020.02.017
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475420300562
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2020.02.017?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. Muhammad Abbas & Ahmad Abd. Majid & Ahmad Izani Md. Ismail & Abdur Rashid, 2014. "Numerical Method Using Cubic Trigonometric B-Spline Technique for Nonclassical Diffusion Problems," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-11, May.
    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. 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.

    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:174:y:2020:i:c:p:32-44. 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.