Abstract and Applied Analysis

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

Allaberen Ashyralyev and Ozgur Yildirim

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Abstract

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.

Article information

Source
Abstr. Appl. Anal., Volume 2012, Special Issue (2012), Article ID 846582, 29 pages.

Dates
First available in Project Euclid: 5 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1365174071

Digital Object Identifier
doi:10.1155/2012/846582

Mathematical Reviews number (MathSciNet)
MR2969985

Zentralblatt MATH identifier
1253.65123

Citation

Ashyralyev, Allaberen; Yildirim, Ozgur. A Note on the Second Order of Accuracy Stable Difference Schemes for the Nonlocal Boundary Value Hyperbolic Problem. Abstr. Appl. Anal. 2012, Special Issue (2012), Article ID 846582, 29 pages. doi:10.1155/2012/846582. https://projecteuclid.org/euclid.aaa/1365174071


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