On Second Order of Accuracy Difference Scheme of the Approximate Solution of Nonlocal Elliptic-Parabolic Problems | Zendy

Allaberen Ashyralyev | Zendy; Okan Gerçek | Zendy

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

Author(s) -

Allaberen Ashyralyev,

Okan Gerçek

Publication year - 2010

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2010/705172

Subject(s) - mathematics , hilbert space , order (exchange) , elliptic operator , mathematical analysis , boundary value problem , operator (biology) , scheme (mathematics) , space (punctuation) , parabolic partial differential equation , partial differential equation , biochemistry , chemistry , linguistics , philosophy , finance , repressor , transcription factor , economics , gene

A second order of accuracy differencescheme for the approximate solution of the abstract nonlocal boundary valueproblem −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 definiteoperator A is considered. The well posedness of this difference scheme in Hölderspaces is established. In applications, coercivity inequalities for the solution of adifference scheme for elliptic-parabolic equations are obtained and a numericalexample is presented

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