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

被引：0

作者：

Ashyralyev, Allaberen ^{[1
]}

Urun, Mesut ^{[2
]}

机构：

[1] Inst Math & Math Modeling, Alma Ata 050010, Kazakhstan

[2] Istanbul Tech Univ, Fac Mech Engn, Istanbul, Turkey

来源：

INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS (ICAAM 2016) | 2016年 / 1759卷

关键词：

Determination of a control parameter problem; Difference scheme; Schrodinger equation; Stability; Well-posedness;

D O I：

10.1063/1.4959700

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the present paper, the second order of accuracy r-modified Crank-Nicholson difference schemes are presented for the numerical solution of the boundary value problem for the Schrodinger differential equation with parameter p {idu(t)/dt + Au(t) + iu(t) - f(t) + p, 0 < t < T, {u(0) = phi, u(T) = psi in a Hilbert space H with self-adjoint positive definite operator A. The well-posedness of this difference scheme is presented. The stability inequalities for the solution of difference schemes for three determination of a control parameter problems for the Schrodinger equation are given.

引用

页数：7

共 24 条

[1] r-Modified Crank-Nicholson difference scheme for fractional parabolic PDE
Ashyralyev, Allaberen
Cakir, Zafer
BOUNDARY VALUE PROBLEMS, 2014,
[2] r-Modified Crank-Nicholson difference scheme for fractional parabolic PDE
Allaberen Ashyralyev
Zafer Cakir
Boundary Value Problems, 2014
[3] r-modified Crank-Nicholson difference schemes for one dimensional nonlinear viscous Burgers' equation for an incompressible flow
Ashyralyev, Allaberen
Gambo, Yusuf Ya'u
INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS (ICAAM 2016), 2016, 1759
[4] On R-Modified Crank-Nicholson Difference Schemes for the Source Identification Parabolic-Elliptic Problem
Ashyralyev, Allaberen
Arikan, Cagin
FOURTH INTERNATIONAL CONFERENCE OF MATHEMATICAL SCIENCES (ICMS 2020), 2021, 2334
[5] On modified Crank-Nicholson difference schemes for stochastic parabolic equation
Ashyralyev, A.
NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2008, 29 (3-4) : 268 - 282
[6] Crank-Nicholson difference scheme for a stochastic parabolic equation with a dependent operator coefficient
Ashyralyev, Allaberen
Okur, Ulker
INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS (ICAAM 2016), 2016, 1759
[7] Modified Crank-Nicholson difference schemes for ultra-parabolic equations
Ashyralyev, Allaberen
Yilmaz, Serhat
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2012, 64 (08) : 2756 - 2764
[8] On the modified Crank-Nicholson difference schemes for parabolic equation with non-smooth data arising in biomechanics
Ashyralyev, Allaberen
Erdogan, Abdullah Said
Arslan, Nurullah
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, 2010, 26 (05) : 501 - 510
[9] Well-posedness of the modified Crank-Nicholson difference schemes in Bochner spaces
Ashyralyev, Allaberen
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2007, 7 (01): : 29 - 51
[10] Modified Crank-Nicholson Difference Schemes for Ultra Parabolic Equations with Neumann Condition
Ashyralyev, Allaberen
Yilmaz, Serhat
NUMERICAL ANALYSIS AND ITS APPLICATIONS, NAA 2012, 2013, 8236 : 182 - 189

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