Title: The finite difference approximations of the optimal control problem for non-linear Schrödinger equation

Authors: Nigar Yıldırım Aksoy; Gabil Yagubov; Bünyamin Yıldız

Addresses: Department of Mathematics, Faculty of Arts and Science, Kafkas University, 36100 Kars, Turkey. ' Department of Mathematics, Faculty of Arts and Science, Kafkas University, 36100 Kars, Turkey. ' Department of Mathematics, Faculty of Arts and Science, Mustafa Kemal University, 31120 Hatay, Turkey

Abstract: In this paper, the finite difference method is applied to the optimal control problem of system governed by non-linear Schrödinger equation. For this purpose, the finite difference scheme is constituted for considered optimal control problem. Obtained an estimation for the solution of this difference scheme, the error of the difference scheme is evaluated. Finally, the convergence according to the functional of the finite difference approximations is proved.

Keywords: nonlinear Schrodinger equation; optimal control; finite difference method; convergence; finite difference approximation.

DOI: 10.1504/IJMMNO.2012.047702

International Journal of Mathematical Modelling and Numerical Optimisation, 2012 Vol.3 No.3, pp.158 - 183

Received: 12 Feb 2011
Accepted: 20 Jun 2011
Published online: 30 Aug 2014 *

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