IDEAS home Printed from https://ideas.repec.org/a/wsi/ijmpcx/v24y2013i03ns0129183113500149.html
   My bibliography  Save this article

Accurately Closed Newton–Cotes Trigonometrically-Fitted Formulae For The Numerical Solution Of The Schrödinger Equation

Author

Listed:
  • T. E. SIMOS

    (Department of Mathematics, College of Sciences, King Saud University, P. O. Box 2455, Riyadh 11451, Saudi Arabia;
    Laboratory of Computational Sciences, Department of Computer Science and Technology, Faculty of Sciences and Technology, University of Peloponnese, GR-221 00 Tripolis, Greece)

Abstract

The investigation on the connection between: (1) closed Newton–Cotes formulae of high-order, (2) trigonometrically-fitted differential schemes and (3) symplectic integrators is presented in this paper. In the last decades, several one step symplectic methods were obtained based on symplectic geometry (see the appropriate literature). The investigation on multistep symplectic integrators is poor. In the present paper: (1) we study a trigonometrically-fitted high-order closed Newton–Cotes formula, (2) we investigate the necessary conditions in a general eight-step differential method to be presented as symplectic multilayer integrator, (3) we present a comparative error analysis in order to show the theoretical superiority of the present method, (4) we apply it to solve the resonance problem of the radial Schrödinger equation. Finally, remarks and conclusions on the efficiency of the new developed method are given which are based on the theoretical and numerical results.

Suggested Citation

  • T. E. Simos, 2013. "Accurately Closed Newton–Cotes Trigonometrically-Fitted Formulae For The Numerical Solution Of The Schrödinger Equation," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 24(03), pages 1-20.
    • Handle: RePEc:wsi:ijmpcx:v:24:y:2013:i:03:n:s0129183113500149
    DOI: 10.1142/S0129183113500149
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0129183113500149
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0129183113500149?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:24:y:2013:i:03:n:s0129183113500149. 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.