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On Stability of a Third Order of Accuracy Difference Scheme for Hyperbolic Nonlocal BVP with Self‐Adjoint Operator

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  • Allaberen Ashyralyev
  • Ozgur Yildirim

Abstract

A third order of accuracy absolutely stable difference schemes is presented for nonlocal boundary value hyperbolic problem of the differential equations in a Hilbert space H with self‐adjoint positive definite operator A. Stability estimates for solution of the difference scheme are established. In practice, one‐dimensional hyperbolic equation with nonlocal boundary conditions is considered.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:959216
    DOI: 10.1155/2013/959216
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    References listed on IDEAS

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    1. 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, Hindawi, vol. 2012, pages 1-29, September.
    2. 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.
    3. 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).
    4. Yildirim Ozdemir & Mehmet Kucukunal, 2012. "A Note on Nonlocal Boundary Value Problems for Hyperbolic Schrödinger Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    5. Yildirim Ozdemir & Mehmet Kucukunal, 2012. "A Note on Nonlocal Boundary Value Problems for Hyperbolic Schrödinger Equations," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-12, June.
    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).
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    Cited by:

    1. 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).

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