A Note on the Second Order of Accuracy Stable Difference Schemes for the Nonlocal Boundary Value Hyperbolic Problem | Zendy

Allaberen Ashyralyev | Zendy; Özgür Yıldırım | Zendy

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A Note on the Second Order of Accuracy Stable Difference Schemes for the Nonlocal Boundary Value Hyperbolic Problem

Author(s) -

Allaberen Ashyralyev,

Özgür Yıldırım

Publication year - 2012

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 - 10.1155/2012/846582

Subject(s) - mathematics , hyperbolic partial differential equation , boundary value problem , mathematical analysis , hilbert space , stability (learning theory) , operator (biology) , order (exchange) , space (punctuation) , boundary (topology) , dirichlet distribution , dirichlet boundary condition , partial differential equation , finance , repressor , machine learning , biochemistry , chemistry , linguistics , philosophy , computer science , transcription factor , economics , gene

The second order of accuracy absolutely stable difference schemes are presented for the nonlocal boundary value hyperbolic problem for the differential equations in a Hilbert space H with the self-adjoint positive definite operator A. The stability estimates for the solutions of these difference schemes are established. In practice, one-dimensional hyperbolic equation with nonlocal boundary conditions and multidimensional hyperbolic equation with Dirichlet conditions are considered. The stability estimates for the solutions of these difference schemes for the nonlocal boundary value hyperbolic problem are established. Finally, a numerical method proposed and numerical experiments, analysis of the errors, and related execution times are presented in order to verify theoretical statements

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