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
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.