Abstract and Applied Analysis

Determination of a Control Parameter for the Difference Schrödinger Equation

Allaberen Ashyralyev and Mesut Urun

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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 ( d u ( t ) / d t ) + A u ( t ) + i u ( t ) = f ( t ) + p , 0 < t < T , u ( 0 ) = φ , u ( T ) = ψ , 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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