IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v330y2018icp103-117.html
   My bibliography  Save this article

Trigonometrically fitted three-derivative Runge–Kutta methods for solving oscillatory initial value problems

Author

Listed:
  • Li, Jiyong

Abstract

Trigonometrically fitted three-derivative Runge–Kutta (TFTHDRK) methods for solving numerically oscillatory initial value problems are proposed and developed. TFTHDRK methods improve three-derivative Runge–Kutta (THDRK) methods [Numer. Algor. 74: 247–265, 2017] and integrate exactly the problem whose solutions can be expressed as the linear combinations of functions from the set of {exp(iwt),exp(−iwt)} or equivalently the set {cos (wt), sin (wt)}, where w approximate the main frequency of the problem. The order conditions are deduced by the theory of rooted trees and B-series and two new explicit special TFTHDRK methods with order five and seven, respectively, are constructed. Linear stability of TFTHDRK methods is examined. Numerical results show the superiority of the new methods over other methods from the scientific literature.

Suggested Citation

  • Li, Jiyong, 2018. "Trigonometrically fitted three-derivative Runge–Kutta methods for solving oscillatory initial value problems," Applied Mathematics and Computation, Elsevier, vol. 330(C), pages 103-117.
    • Handle: RePEc:eee:apmaco:v:330:y:2018:i:c:p:103-117
    DOI: 10.1016/j.amc.2018.01.017
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300318300304
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2018.01.017?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.

    Citations

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


    Cited by:

    1. Faieza Samat & Eddie Shahril Ismail, 2021. "Modified Hybrid Method with Four Stages for Second Order Ordinary Differential Equations," Mathematics, MDPI, vol. 9(9), pages 1-7, May.
    2. Higinio Ramos & Ridwanulahi Abdulganiy & Ruth Olowe & Samuel Jator, 2021. "A Family of Functionally-Fitted Third Derivative Block Falkner Methods for Solving Second-Order Initial-Value Problems with Oscillating Solutions," Mathematics, MDPI, vol. 9(7), pages 1-22, March.

    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:apmaco:v:330:y:2018:i:c:p:103-117. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.