Stability of a Second Order of Accuracy Difference Scheme for Hyperbolic Equation in a Hilbert SpaceReport as inadecuate




Stability of a Second Order of Accuracy Difference Scheme for Hyperbolic Equation in a Hilbert Space - Download this document for free, or read online. Document in PDF available to download.

Discrete Dynamics in Nature and Society - Volume 2007 2007, Article ID 57491, 25 pages

Research Article

Department of Mathematics, Fatih University, Buyukcekmece, Istanbul 34900, Turkey

Graduate Institute of Sciences and Engineering, Fatih University, Buyukcekmece, Istanbul 34900, Turkey

Department of Mathematics, Gebze Institute of Technology, Gebze-Kocaeli 41400, Turkey

Received 7 June 2007; Accepted 16 September 2007

Copyright © 2007 Allaberen Ashyralyev and Mehmet Emir Koksal. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The initial-value problem for hyperbolic equationd2ut-dt2+Atut=ft0≤t≤T, u0=ϕ,u′0=ψ in a Hilbert space H with the self-adjoint positive definite operators At is considered. The second order of accuracy difference scheme for the approximately solving this initial-value problem is presented. The stability estimates for the solution of this difference scheme are established.





Author: Allaberen Ashyralyev and Mehmet Emir Koksal

Source: https://www.hindawi.com/



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