IDEAS home Printed from https://ideas.repec.org/a/wsi/ijmpcx/v06y1995i01ns0129183195000125.html
   My bibliography  Save this article

Spectral Properties Of Derivative Operators In The Basis-Spline Collocation Method

Author

Listed:
  • J.C. WELLS

    (Center for Computationally Intensive Physics, Physics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831–6373, USA)

  • V.E. OBERACKER

    (Center for Computationally Intensive Physics, Physics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831–6373, USA)

  • M.R. STRAYER

    (Center for Computationally Intensive Physics, Physics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831–6373, USA)

  • A.S. UMAR

    (Center for Computationally Intensive Physics, Physics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831–6373, USA)

Abstract

We discuss the basis-spline collocation method for the lattice solution of boundary-value differential equations, drawing particular attention to the difference between lattice and continuous collocation methods. Spectral properties of the basis-spline lattice representation of the first and second spatial derivatives are studied for the case of periodic boundary conditions with homogeneous lattice spacing and compared to spectra obtained using traditional finite-difference schemes. Basis-spline representations are shown to give excellent resolution on small-length scales and to satisfy the chain rule with good fidelity for the lattice-derivative operators using high-order splines. Application to the one-dimensional Dirac equation shows that very high-order spline representations of the Hamiltonian on odd lattices avoid the notorious spectral-doubling problem.

Suggested Citation

  • J.C. Wells & V.E. Oberacker & M.R. Strayer & A.S. Umar, 1995. "Spectral Properties Of Derivative Operators In The Basis-Spline Collocation Method," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 6(01), pages 143-167.
    • Handle: RePEc:wsi:ijmpcx:v:06:y:1995:i:01:n:s0129183195000125
    DOI: 10.1142/S0129183195000125
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0129183195000125
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0129183195000125?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

    for a different version of it.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:06:y:1995:i:01:n:s0129183195000125. 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.