IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i2p213-d317865.html
   My bibliography  Save this article

Asymptotic Convergence of the Solution of a Singularly Perturbed Integro-Differential Boundary Value Problem

Author

Listed:
  • Assiya Zhumanazarova

    (Department of Computer Engineering, Gachon University, Gyeonggi-do 461-701, Korea)

  • Young Im Cho

    (Department of Computer Engineering, Gachon University, Gyeonggi-do 461-701, Korea)

Abstract

In this study, the asymptotic behavior of the solutions to a boundary value problem for a third-order linear integro-differential equation with a small parameter at the two higher derivatives has been examined, under the condition that the roots of the additional characteristic equation are negative. Via the scheme of methods and algorithms pertaining to the qualitative study of singularly perturbed problems with initial jumps, a fundamental system of solutions, the Cauchy function, and the boundary functions of a homogeneous singularly perturbed differential equation are constructed. Analytical formulae for the solutions and asymptotic estimates of the singularly perturbed problem are obtained. Furthermore, a modified degenerate boundary value problem has been constructed, and it was stated that the solution of the original singularly perturbed boundary value problem tends to this modified problem’s solution.

Suggested Citation

  • Assiya Zhumanazarova & Young Im Cho, 2020. "Asymptotic Convergence of the Solution of a Singularly Perturbed Integro-Differential Boundary Value Problem," Mathematics, MDPI, vol. 8(2), pages 1-17, February.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:2:p:213-:d:317865
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/2/213/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/2/213/
    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:2:p:213-:d:317865. 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.