IDEAS home Printed from https://ideas.repec.org/a/hin/jnlaaa/513959.html
   My bibliography  Save this article

Accurate solution estimates for nonlinear nonautonomous vector difference equations

Author

Listed:
  • Rigoberto Medina
  • M. I. Gil'

Abstract

The paper deals with the vector discrete dynamical system x k + 1 = A k x k + f k ( x k ) . Thewell-known result by Perron states that this system is asymptotically stable if A k ≡ A = const is stable and f k ( x ) ≡ f ˜ ( x ) = o ( ‖ x ‖ ) . Perron's result gives no information about the size of the region of asymptotic stability and norms of solutions. In this paper, accurate estimates for the norms of solutions are derived. They give us stability conditions for (1.1) and bounds for the region of attraction of the stationary solution. Our approach is based on the freezing method for difference equations and on recent estimates for the powers of a constant matrix. We also discuss applications of our main result to partial reaction-diffusion difference equations.

Suggested Citation

  • Rigoberto Medina & M. I. Gil', 2004. "Accurate solution estimates for nonlinear nonautonomous vector difference equations," Abstract and Applied Analysis, Hindawi, vol. 2004, pages 1-9, January.
    • Handle: RePEc:hin:jnlaaa:513959
    DOI: 10.1155/S1085337504306184
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/AAA/2004/513959.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/AAA/2004/513959.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/S1085337504306184?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
    ---><---

    Citations

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


    Cited by:

    1. Rigoberto Medina, 2014. "Exponential Stability Criteria for Nonautonomous Difference Systems," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2014, pages 1-7, April.

    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:hin:jnlaaa:513959. 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: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.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.