Abstract and Applied Analysis

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

Allaberen Ashyralyev and Okan Gercek

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Abstract

A second order of accuracy difference scheme for the approximate solution of the abstract nonlocal boundary value problem d 2 u ( t ) / d t 2 + A u ( t ) = g ( t ) , ( 0 t 1 ) , d u ( t ) / d t A u ( 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.

Article information

Source
Abstr. Appl. Anal., Volume 2010 (2010), Article ID 705172, 17 pages.

Dates
First available in Project Euclid: 1 November 2010

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1288620744

Digital Object Identifier
doi:10.1155/2010/705172

Mathematical Reviews number (MathSciNet)
MR2669087

Zentralblatt MATH identifier
1198.65120

Citation

Ashyralyev, Allaberen; Gercek, Okan. On Second Order of Accuracy Difference Scheme of the Approximate Solution of Nonlocal Elliptic-Parabolic Problems. Abstr. Appl. Anal. 2010 (2010), Article ID 705172, 17 pages. doi:10.1155/2010/705172. https://projecteuclid.org/euclid.aaa/1288620744


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