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A note on the difference schemes for hyperbolic‐elliptic equations

Author

Listed:
  • A. Ashyralyev
  • G. Judakova
  • P. E. Sobolevskii

Abstract

The nonlocal boundary value problem for hyperbolic‐elliptic equation d2u(t)/dt2 + Au(t) = f(t), (0 ≤ t ≤ 1), −d2u(t)/dt2 + Au(t) = g(t), (−1 ≤ t ≤ 0), u(0) = ϕ, u(1) = u(−1) in a Hilbert space H is considered. The second order of accuracy difference schemes for approximate solutions of this boundary value problem are presented. The stability estimates for the solution of these difference schemes are established.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnlaaa:v:2006:y:2006:i:1:n:014816
    DOI: 10.1155/AAA/2006/14816
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    References listed on IDEAS

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    1. 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.
    2. A. Ashyralyev & A. Hanalyev & P. E. Sobolevskii, 2001. "Coercive solvability of the nonlocal boundary value problem for parabolic differential equations," Abstract and Applied Analysis, Hindawi, vol. 6, pages 1-9, January.
    3. 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.
    4. A. Ashyralyev & A. Hanalyev & P. E. Sobolevskii, 2001. "Coercive solvability of the nonlocal boundary value problem for parabolic differential equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 6(1), pages 53-61.
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    Citations

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    Cited by:

    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. 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).
    3. 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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