Determination of a Control Parameter for the Difference Schrödinger Equation

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<t<T, u(0)=φ, u(T)=ψ, in a Hilbert space H with self-adjoint positive definite operator A is constructed. The...

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Bibliographic Details
Main Authors: Allaberen Ashyralyev, Mesut Urun
Format: Article
Language:English
Published: Wiley 2013-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2013/548201
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Summary: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<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.
ISSN:1085-3375
1687-0409