Abstract and Applied Analysis
Volume 2012 (2012), Article ID 684248, 24 pages
http://dx.doi.org/10.1155/2012/684248
Research Article

An Approximation of Semigroups Method for Stochastic Parabolic Equations

Allaberen Ashyralyev1,2 and Mehmet Emin San3

1Department of Mathematics, Fatih University, Buyukcekmece, 34500 Istanbul, Turkey
2Department of Mathematics, ITTU, 74012 Ashgabat, Turkmenistan
3Certified Dental Supply LLC 43 River Road, Nutley, NJ 07031, USA

Received 25 May 2012; Accepted 8 June 2012

Academic Editor: Ravshan Ashurov

Copyright © 2012 Allaberen Ashyralyev and Mehmet Emin San. 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

A single-step difference scheme for the numerical solution of the nonlocal-boundary value problem for stochastic parabolic equations is presented. The convergence estimate for the solution of the difference scheme is established. In application, the convergence estimates for the solution of the difference scheme are obtained for two nonlocal-boundary value problems. The theoretical statements for the solution of this difference scheme are supported by numerical examples.