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

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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.

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