IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v205y2023icp142-185.html
   My bibliography  Save this article

Numerical methods, energy conservation, and a new method for particle motion in magnetic fields

Author

Listed:
  • Arendt, V.

Abstract

This article mathematically examines the energy conservation of explicit Runge–Kutta methods and basic symplectic integration methods for a simple harmonic oscillator and a particle in a magnetic field. With the demonstration of the failure of these methods to conserve the energy of a particle in a magnetic field, a new integration method is presented for this type of system where energy conservation is dictated by the type of floating point variable used, not the size of the time step or the method order. Higher order versions of the method improve the accuracy in the calculation of the particle position and allow for more accurate calculations of the velocity in a spatially varying field. Furthermore, the new method is demonstrated to have improved phase accuracy when compared to several common implicit methods.

Suggested Citation

  • Arendt, V., 2023. "Numerical methods, energy conservation, and a new method for particle motion in magnetic fields," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 142-185.
    • Handle: RePEc:eee:matcom:v:205:y:2023:i:c:p:142-185
    DOI: 10.1016/j.matcom.2022.09.015
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475422003925
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2022.09.015?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:eee:matcom:v:205:y:2023:i:c:p:142-185. 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: 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.