Determination of a control parameter of the r-modified Crank-Nicholson difference scheme for the Schrödinger equation

2016 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Mesut Urun
Keyword(s):  
Schrödinger Equation ◽  
Difference Scheme ◽  
Schrodinger Equation ◽  
Control Parameter

scholarly journals Determination of a Control Parameter for the Difference Schrödinger Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Mesut Urun
Keyword(s):  
Schrödinger Equation ◽  
Difference Scheme ◽  
Schrodinger Equation ◽  
Control Parameter ◽  
Order Of Accuracy ◽  
Definite Operator ◽  
Accuracy Difference ◽  
The Difference ◽  
The Stability

The first order of accuracy difference scheme for the numerical solution of the boundary value problem for the differential equation with parameterp,i(du(t)/dt)+Au(t)+iu(t)=f(t)+p,0<t<T,u(0)=φ,u(T)=ψ, in a Hilbert spaceHwith self-adjoint positive definite operatorAis 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.

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