IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2025i11p1833-d1668602.html
   My bibliography  Save this article

Efficient 5-Point Block Method for Oscillatory ODEs with Phase Lag and Amplification Error Control

Author

Listed:
  • Rubayyi T. Alqahtani

    (Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11623, Saudi Arabia)

  • Anurag Kaur

    (School of Mathematics, Thapar Institute of Engineering and Technology (Deemed University), Patiala 147004, Punjab, India)

  • Theodore E. Simos

    (Center for Applied Mathematics and Bioinformatics, Gulf University for Science and Technology, Hawally 32093, Kuwait)

Abstract

This research presents innovative modified explicit block methods with fifth-order algebraic accuracy to address initial value problems (IVPs). The derivation of the methods employs fitting coefficients that eliminate phase lag and amplification error, as well as their derivatives. A thorough stability analysis of the new approach is conducted. Comparative assessments with existing methods highlight the superior effectiveness of the proposed algorithms. Numerical tests verify that this technique significantly surpasses conventional methods for solving IVPs, particularly those exhibiting oscillatory solutions.

Suggested Citation

  • Rubayyi T. Alqahtani & Anurag Kaur & Theodore E. Simos, 2025. "Efficient 5-Point Block Method for Oscillatory ODEs with Phase Lag and Amplification Error Control," Mathematics, MDPI, vol. 13(11), pages 1-41, May.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:11:p:1833-:d:1668602
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/11/1833/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/11/1833/
    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:13:y:2025:i:11:p:1833-:d:1668602. 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.