## Abstract and Applied Analysis

### Determination of a Control Parameter for the Difference Schrödinger Equation

#### Abstract

The first order of accuracy difference scheme for the numerical solution of the boundary value problem for the differential equation with parameter $p$, $i(du(t)/dt)+Au(t)+iu(t)=f(t)+p$, $0, $u(0)=\phi$, $u(T)=\psi$, in a Hilbert space $H$ with self-adjoint positive definite operator $A$ 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.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 548201, 8 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393450130

Digital Object Identifier
doi:10.1155/2013/548201

Mathematical Reviews number (MathSciNet)
MR3126791

Zentralblatt MATH identifier
1291.65091

#### Citation

Ashyralyev, Allaberen; Urun, Mesut. Determination of a Control Parameter for the Difference Schrödinger Equation. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 548201, 8 pages. doi:10.1155/2013/548201. https://projecteuclid.org/euclid.aaa/1393450130

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