IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v190y2021icp760-773.html
   My bibliography  Save this article

A hybrid augmented compact finite volume method for the Thomas–Fermi equation

Author

Listed:
  • Zhao, Tengjin
  • Zhang, Zhiyue
  • Wang, Tongke

Abstract

A new efficient method that combines the Puiseux series asymptotic technique with an augmented compact finite volume method is proposed to develop a numerical approximate solution for the Thomas–Fermi equation on semi-infinity domain. By using the asymptotic series of solution at infinity and the Puiseux series expansion at origin to characterize the singularities, the natural and precise boundary conditions are obtained. The expansions contain undetermined parameters which associate with the singularity as the augmented variables. A regular boundary value problem is derived, for which an augmented compact finite volume method is used. The computational results show that the method not only obtains the high precise numerical solution, but also obtains the high precise initial slope. In particular, we find that the initial slope is exactly equal to the augmented variable related to the singularities in the Puiseux series. The initial slope not only has an important physical significance, but also its calculation accuracy has become an important criteria to measure the quality of the algorithm.

Suggested Citation

  • Zhao, Tengjin & Zhang, Zhiyue & Wang, Tongke, 2021. "A hybrid augmented compact finite volume method for the Thomas–Fermi equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 760-773.
    • Handle: RePEc:eee:matcom:v:190:y:2021:i:c:p:760-773
    DOI: 10.1016/j.matcom.2021.06.010
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475421002330
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2021.06.010?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.

    References listed on IDEAS

    as
    1. Amore, Paolo & Boyd, John P. & Fernández, Francisco M., 2014. "Accurate calculation of the solutions to the Thomas–Fermi equations," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 929-943.
    2. Wang, Tongke & Zhang, Zhiyue, 2015. "A compact finite volume method and its extrapolation for elliptic equations with third boundary conditions," Applied Mathematics and Computation, Elsevier, vol. 264(C), pages 258-271.
    3. Zhao, Tengjin & Zhang, Zhiyue & Wang, Tongke, 2021. "A hybrid asymptotic and augmented compact finite volume method for nonlinear singular two point boundary value problems," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Peng, Jie & Shu, Shi & Yu, HaiYuan & Feng, Chunsheng & Kan, Mingxian & Wang, Ganghua, 2017. "Error estimates on a finite volume method for diffusion problems with interface on rectangular grids," Applied Mathematics and Computation, Elsevier, vol. 311(C), pages 335-352.
    2. Zhao, Tengjin & Zhang, Zhiyue & Wang, Tongke, 2021. "A hybrid asymptotic and augmented compact finite volume method for nonlinear singular two point boundary value problems," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    3. Seiler, Werner M. & Seiß, Matthias, 2024. "On the numerical integration of singular initial and boundary value problems for generalised Lane–Emden and Thomas–Fermi equations," Applied Mathematics and Computation, Elsevier, vol. 466(C).

    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:190:y:2021:i:c:p:760-773. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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.