IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i9p1571-d412423.html
   My bibliography  Save this article

Numerical Solution of Stieltjes Differential Equations

Author

Listed:
  • Francisco J. Fernández

    (Instituto de Matemáticas, Universidade de Santiago de Compostela, 15705 Santiago de Compostela, Spain
    These authors contributed equally to this work.)

  • F. Adrián F. Tojo

    (Instituto de Matemáticas, Universidade de Santiago de Compostela, 15705 Santiago de Compostela, Spain
    These authors contributed equally to this work.)

Abstract

This work is devoted to the obtaining of a new numerical scheme based on quadrature formulae for the Lebesgue–Stieltjes integral for the approximation of Stieltjes ordinary differential equations. This novel method allows us to numerically approximate models based on Stieltjes ordinary differential equations for which no explicit solution is known. We prove several theoretical results related to the consistency, convergence, and stability of the numerical method. We also obtain the explicit solution of the Stieltjes linear ordinary differential equation and use it to validate the numerical method. Finally, we present some numerical results that we have obtained for a realistic population model based on a Stieltjes differential equation and a system of Stieltjes differential equations with several derivators.

Suggested Citation

  • Francisco J. Fernández & F. Adrián F. Tojo, 2020. "Numerical Solution of Stieltjes Differential Equations," Mathematics, MDPI, vol. 8(9), pages 1-30, September.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:9:p:1571-:d:412423
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/9/1571/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/9/1571/
    Download Restriction: no
    ---><---

    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:gam:jmathe:v:8:y:2020:i:9:p:1571-:d:412423. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.