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On Second Order of Accuracy Difference Scheme of the Approximate Solution of Nonlocal Elliptic‐Parabolic Problems

Author

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  • Allaberen Ashyralyev
  • Okan Gercek

Abstract

A second order of accuracy difference scheme for the approximate solution of the abstract nonlocal boundary value problem −d2u(t)/dt2 + Au(t) = g(t), (0 ≤ t ≤ 1), du(t)/dt − Au(t) = f(t), (−1 ≤ t ≤ 0), u(1) = u(−1) + μ for differential equations in a Hilbert space H with a self‐adjoint positive definite operator A is considered. The well posedness of this difference scheme in Hölder spaces is established. In applications, coercivity inequalities for the solution of a difference scheme for elliptic‐parabolic equations are obtained and a numerical example is presented.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnlaaa:v:2010:y:2010:i:1:n:705172
    DOI: 10.1155/2010/705172
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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. 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).
    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. 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).

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