IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v5y2017i2p28-d99339.html
   My bibliography  Save this article

A Two-Stage Method for Piecewise-Constant Solution for Fredholm Integral Equations of the First Kind

Author

Listed:
  • Fu-Rong Lin

    (Department of Mathematics, Shantou University, Shantou 515063, China)

  • Shi-Wei Yang

    (Department of Mathematics, Shantou University, Shantou 515063, China)

Abstract

A numerical method is proposed for estimating piecewise-constant solutions for Fredholm integral equations of the first kind. Two functionals, namely the weighted total variation (WTV) functional and the simplified Modica-Mortola (MM) functional, are introduced. The solution procedure consists of two stages. In the first stage, the WTV functional is minimized to obtain an approximate solution f TV * . In the second stage, the simplified MM functional is minimized to obtain the final result by using the damped Newton (DN) method with f TV * as the initial guess. The numerical implementation is given in detail, and numerical results of two examples are presented to illustrate the efficiency of the proposed approach.

Suggested Citation

  • Fu-Rong Lin & Shi-Wei Yang, 2017. "A Two-Stage Method for Piecewise-Constant Solution for Fredholm Integral Equations of the First Kind," Mathematics, MDPI, vol. 5(2), pages 1-16, May.
    • Handle: RePEc:gam:jmathe:v:5:y:2017:i:2:p:28-:d:99339
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/5/2/28/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/5/2/28/
    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:5:y:2017:i:2:p:28-:d:99339. 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.