IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-0-8176-4897-8_11.html

Modified Newton’s Methods for Systems of Nonlinear Equations

In: Integral Methods in Science and Engineering, Volume 2

Author

Listed:
  • A. Cordero

    (Universidad Politécnica de Valencia)

  • J. R. Torregrosa

    (Universidad Politécnica de Valencia)

Abstract

The main goal of this chapter is to obtain new iterative formulas in order to solve systems of nonlinear equations. They are proved to be modifications on classical Newton’s method which accelerate the convergence of the iterative process. In previous works, the authors have obtained variants on Newton’s method based on quadrature formulas whose truncation error was up to O(h 5) (see [CoTo06] and [CoTo07]). Nevertheless, the approach used in this paper to solve a nonlinear system is different: by using Adomian polynomials, we obtain a family of multipoint iterative formulas, which include Newton and Traub (see [Tr82]) methods in the simplest cases. The decomposition method using Adomian polynomials is used to solve different problems in applied mathematics in [Ad88]. Indeed, Babolian et al. (see [BaBiVa04]) apply this general method to a concrete nonlinear system. Nevertheless, with a different system, it is necessary to reconstruct the entire process.

Suggested Citation

  • A. Cordero & J. R. Torregrosa, 2010. "Modified Newton’s Methods for Systems of Nonlinear Equations," Springer Books, in: Christian Constanda & M.E. Pérez (ed.), Integral Methods in Science and Engineering, Volume 2, chapter 11, pages 121-130, Springer.
    • Handle: RePEc:spr:sprchp:978-0-8176-4897-8_11
    DOI: 10.1007/978-0-8176-4897-8_11
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Statistics

    Access and download statistics

    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:spr:sprchp:978-0-8176-4897-8_11. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.