IDEAS home Printed from https://ideas.repec.org/a/wly/jnlaaa/v2012y2012i1n846582.html

A Note on the Second Order of Accuracy Stable Difference Schemes for the Nonlocal Boundary Value Hyperbolic Problem

Author

Listed:
  • Allaberen Ashyralyev
  • Ozgur Yildirim

Abstract

The second order of accuracy absolutely stable difference schemes are presented for the nonlocal boundary value hyperbolic problem for the differential equations in a Hilbert space H with the self‐adjoint positive definite operator A. The stability estimates for the solutions of these difference schemes are established. In practice, one‐dimensional hyperbolic equation with nonlocal boundary conditions and multidimensional hyperbolic equation with Dirichlet conditions are considered. The stability estimates for the solutions of these difference schemes for the nonlocal boundary value hyperbolic problem are established. Finally, a numerical method proposed and numerical experiments, analysis of the errors, and related execution times are presented in order to verify theoretical statements.

Suggested Citation

  • Allaberen Ashyralyev & Ozgur Yildirim, 2012. "A Note on the Second Order of Accuracy Stable Difference Schemes for the Nonlocal Boundary Value Hyperbolic Problem," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:846582
    DOI: 10.1155/2012/846582
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2012/846582
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2012/846582?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
    ---><---

    References listed on IDEAS

    as
    1. Allaberen Ashyralyev & Okan Gercek, 2010. "On Second Order of Accuracy Difference Scheme of the Approximate Solution of Nonlocal Elliptic-Parabolic Problems," Abstract and Applied Analysis, Hindawi, vol. 2010, pages 1-17, July.
    2. A. Ashyralyev & P. E. Sobolevskii, 2001. "A note on the difference schemes for hyperbolic equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 6(2), pages 63-70.
    3. A. Ashyralyev & G. Judakova & P. E. Sobolevskii, 2006. "A note on the difference schemes for hyperbolic‐elliptic equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2006(1).
    4. A. Ashyralyev & G. Judakova & P. E. Sobolevskii, 2006. "A note on the difference schemes for hyperbolic-elliptic equations," Abstract and Applied Analysis, Hindawi, vol. 2006, pages 1-13, February.
    5. A. Ashyralyev & P. E. Sobolevskii, 2001. "A note on the difference schemes for hyperbolic equations," Abstract and Applied Analysis, Hindawi, vol. 6, pages 1-8, January.
    6. Allaberen Ashyralyev & Okan Gercek, 2010. "On Second Order of Accuracy Difference Scheme of the Approximate Solution of Nonlocal Elliptic‐Parabolic Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Allaberen Ashyralyev & Ozgur Yildirim, 2013. "On Stability of a Third Order of Accuracy Difference Scheme for Hyperbolic Nonlocal BVP with Self‐Adjoint Operator," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. A. Ashyralyev & J. Pastor & S. Piskarev & H. A. Yurtsever, 2015. "Second Order Equations in Functional Spaces: Qualitative and Discrete Well‐Posedness," Abstract and Applied Analysis, John Wiley & Sons, vol. 2015(1).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Allaberen Ashyralyev & Okan Gercek, 2012. "On the Second Order of Accuracy Stable Implicit Difference Scheme for Elliptic‐Parabolic Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    2. A. Ashyralyev & J. Pastor & S. Piskarev & H. A. Yurtsever, 2015. "Second Order Equations in Functional Spaces: Qualitative and Discrete Well‐Posedness," Abstract and Applied Analysis, John Wiley & Sons, vol. 2015(1).
    3. A. Ashyralyev & G. Judakova & P. E. Sobolevskii, 2006. "A note on the difference schemes for hyperbolic‐elliptic equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2006(1).
    4. Okan Gercek, 2012. "Well‐Posedness of the First Order of Accuracy Difference Scheme for Elliptic‐Parabolic Equations in Hölder Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    5. Allaberen Ashyralyev & Ozgur Yildirim, 2013. "On Stability of a Third Order of Accuracy Difference Scheme for Hyperbolic Nonlocal BVP with Self‐Adjoint Operator," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    6. Ozgur Yildirim & Meltem Uzun, 2015. "On Third Order Stable Difference Scheme for Hyperbolic Multipoint Nonlocal Boundary Value Problem," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-16, July.

    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:wly:jnlaaa:v:2012:y:2012:i:1:n:846582. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/4058 .

    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.