About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 548201, 8 pages
http://dx.doi.org/10.1155/2013/548201
Research Article

Determination of a Control Parameter for the Difference Schrödinger Equation

1Department of Mathematics, Fatih University, Buyukcekmece, 34500 Istanbul, Turkey
2ITTU, 32 Gerogly Street, 74400 Ashgabat, Turkmenistan
3Department of Mathematics, Murat Education Institution, 34353 Istanbul, Turkey

Received 28 July 2013; Accepted 18 September 2013

Academic Editor: Abdullah Said Erdogan

Copyright © 2013 Allaberen Ashyralyev and Mesut Urun. 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 order of accuracy difference scheme for the numerical solution of the boundary value problem for the differential equation with parameter , , , , , in a Hilbert space with self-adjoint positive definite operator is constructed. The well-posedness of this difference scheme is established. The stability inequalities for the solution of difference schemes for three different types of control parameter problems for the Schrödinger equation are obtained.