IDEAS home Printed from https://ideas.repec.org/a/wsi/ijmpcx/v30y2019i12ns0129183119501018.html
   My bibliography  Save this article

An adaptive grid-based curvelet optimized solution for nonlinear Schrödinger equation

Author

Listed:
  • Deepika Sharma

    (#x2020;School of Mathematics, Thapar Institute of Engineering and Technology, Patiala, Punjab, India)

  • Rohit K. Singla

    (Mechanical Engineering Department, Thapar Institute of Engineering and Technology, Patiala, Punjab, India)

  • Kavita Goyal

    (#x2020;School of Mathematics, Thapar Institute of Engineering and Technology, Patiala, Punjab, India)

Abstract

In this work, a dynamically adaptive curvelet technique has been developed for solving nonlinear Schrödinger equation (NLS). Central finite difference method is used for approximating the one- and two-dimensional differential operators and radial-basis functions (RBFs) are utilized for approximating the differential operators on the sphere. The grid on which the equation is solved, is obtained using curvelets. For test problems 1 and 2 (1d & 2d problems) considered in this paper, the computational time carried out by the proposed technique is analyzed with the computational time carried out by the finite difference technique. Moreover, the problem on the sphere has been considered, for which the computational time carried out by the RBF collocation technique is analyzed with the computational time carried out by the proposed technique. It is found that the developed technique performs better in terms of computational time, for example, on sphere, computational effort reduces by four times using the proposed method.

Suggested Citation

  • Deepika Sharma & Rohit K. Singla & Kavita Goyal, 2019. "An adaptive grid-based curvelet optimized solution for nonlinear Schrödinger equation," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 30(12), pages 1-28, December.
    • Handle: RePEc:wsi:ijmpcx:v:30:y:2019:i:12:n:s0129183119501018
    DOI: 10.1142/S0129183119501018
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0129183119501018
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0129183119501018?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.

    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:wsi:ijmpcx:v:30:y:2019:i:12:n:s0129183119501018. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/ijmpc/ijmpc.shtml .

    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.