IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i14p2287-d1440218.html
   My bibliography  Save this article

On the Selection of Weights for Difference Schemes to Approximate Systems of Differential Equations

Author

Listed:
  • Viktor Kadrov

    (Department of Computational Mathematics and Artificial Intelligence, RUDN University, 117198 Moscow, Russia)

  • Mikhail Malykh

    (Department of Computational Mathematics and Artificial Intelligence, RUDN University, 117198 Moscow, Russia
    Meshcheryakov Laboratory of Information Technologies, Joint Institute for Nuclear Research, 141980 Dubna, Russia)

  • Alexander Zorin

    (Department of Computational Mathematics and Artificial Intelligence, RUDN University, 117198 Moscow, Russia)

Abstract

We consider the problem of determining the weights of difference schemes whose form is specified by a particular symbolic expression. The order of approximation of the differential equation is equal to a given number. To solve it, it was propose to proceed from considering systems of differential equations of a general form to one scalar equation. This method provides us with some values for the weights, which we propose to test using Richardson’s method. The method was shown to work in the case of low-order schemes. However, when transitioning from the scalar problem to the vector and nonlinear problems, the reduction of the order of the scheme, whose weights are selected for the scalar problem, occurs in different families of schemes. This was first discovered when studying the Shanks scheme, which belongs to the family of explicit Runge–Kutta schemes. This does not deteriorate the proposed strategy itself concerning the simplification of the weight-determination problem, which should include a clause on mandatory testing of the order using the Richardson method.

Suggested Citation

  • Viktor Kadrov & Mikhail Malykh & Alexander Zorin, 2024. "On the Selection of Weights for Difference Schemes to Approximate Systems of Differential Equations," Mathematics, MDPI, vol. 12(14), pages 1-11, July.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:14:p:2287-:d:1440218
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/14/2287/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/14/2287/
    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:12:y:2024:i:14:p:2287-:d:1440218. 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.