IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i3p306-d728307.html
   My bibliography  Save this article

Comparison of the Selected Methods Used for Solving the Ordinary Differential Equations and Their Systems

Author

Listed:
  • Edyta Hetmaniok

    (Faculty of Applied Mathematics, Silesian Technical University of Gliwice, 44-100 Gliwice, Slaskie, Poland
    These authors contributed equally to this work.)

  • Mariusz Pleszczyński

    (Faculty of Applied Mathematics, Silesian Technical University of Gliwice, 44-100 Gliwice, Slaskie, Poland
    These authors contributed equally to this work.)

Abstract

Ordinary differential equations (ODEs), and the systems of such equations, are used for describing many essential physical phenomena. Therefore, the ability to efficiently solve such tasks is important and desired. The goal of this paper is to compare three methods devoted to solving ODEs and their systems, with respect to the quality of obtained solutions, as well as the speed and reliability of working. These approaches are the classical and often applied Runge–Kutta method of order 4 (RK4), the method developed on the ground of the Taylor series, the differential transformation method (DTM), and the routine available in the Mathematica software (Mat).

Suggested Citation

  • Edyta Hetmaniok & Mariusz Pleszczyński, 2022. "Comparison of the Selected Methods Used for Solving the Ordinary Differential Equations and Their Systems," Mathematics, MDPI, vol. 10(3), pages 1-15, January.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:3:p:306-:d:728307
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/3/306/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/3/306/
    Download Restriction: no
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Rafał Brociek & Mariusz Pleszczyński, 2024. "Differential Transform Method and Neural Network for Solving Variational Calculus Problems," Mathematics, MDPI, vol. 12(14), pages 1-13, July.
    2. Saeed Althubiti & Abdelaziz Mennouni, 2022. "A Novel Projection Method for Cauchy-Type Systems of Singular Integro-Differential Equations," Mathematics, MDPI, vol. 10(15), pages 1-11, July.
    3. Abu-Ghuwaleh, Mohammad & Saadeh, Rania & Saffaf, Rasheed, 2024. "Master generators: A novel approach to construct and solve ordinary differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 218(C), pages 600-623.

    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:10:y:2022:i:3:p:306-:d:728307. 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.