IDEAS home Printed from https://ideas.repec.org/a/wsi/ijmpcx/v14y2003i08ns0129183103005194.html
   My bibliography  Save this article

A Twelfth-Order Four-Step Formula For The Numerical Integration Of The One-Dimensional Schrödinger Equation

Author

Listed:
  • ZHONGCHENG WANG

    (Department of Physics, Shanghai University, 99 ShangDa Road, Shanghai 200436, P. R. China)

  • YONGMING DAI

    (Department of Physics, Shanghai University, 99 ShangDa Road, Shanghai 200436, P. R. China)

Abstract

A new twelfth-order four-step formula containing fourth derivatives for the numerical integration of the one-dimensional Schrödinger equation has been developed. It was found that by adding multi-derivative terms, the stability of a linear multi-step method can be improved and the interval of periodicity of this new method is larger than that of the Numerov's method. The numerical test shows that the new method is superior to the previous lower orders in both accuracy and efficiency and it is specially applied to the problem when an increasing accuracy is requested.

Suggested Citation

  • Zhongcheng Wang & Yongming Dai, 2003. "A Twelfth-Order Four-Step Formula For The Numerical Integration Of The One-Dimensional Schrödinger Equation," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 14(08), pages 1087-1105.
    • Handle: RePEc:wsi:ijmpcx:v:14:y:2003:i:08:n:s0129183103005194
    DOI: 10.1142/S0129183103005194
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0129183103005194
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0129183103005194?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:14:y:2003:i:08:n:s0129183103005194. 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.