Mathematical Problems in Engineering
Volume 2007 (2007), Article ID 90815, 16 pages
doi:10.1155/2007/90815
Research Article

Well-Posedness of the Boundary Value Problem for Parabolic Equations in Difference Analogues of Spaces of Smooth Functions

A. Ashyralyev

Department of Mathematics, Faculty of Arts and Science, Fatih University, Istanbul 34900, Turkey

Received 15 June 2006; Accepted 27 December 2006

Academic Editor: F. E. Udwadia

Copyright © 2007 A. Ashyralyev. 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 first and second orders of accuracy difference schemes for the approximate solutions of the nonlocal boundary value problem v′(t)+Av(t)=f(t) (0≤t≤1), v(0)=v(λ)+μ, 0<λ≤1, for differential equation in an arbitrary Banach space E with the strongly positive operator A are considered. The well-posedness of these difference schemes in difference analogues of spaces of smooth functions is established. In applications, the coercive stability estimates for the solutions of difference schemes for the approximate solutions of the nonlocal boundary value problem for parabolic equation are obtained.