On a Stability Theorem of the Optimal Control Problem For Quasi Optic Equation

Yusuf Kocak; Ercan Celik; Nigar Yildrim Aksoy

Yusuf Kocak University of Agri Ibrahim Cecen, Faculty of Science and Letters, Department of Mathematics, Agrı Turkey
Ercan Celik Department of Mathematics, Faculty of Science, Ataturk University, Erzurum, Turkey
Nigar Yildrim Aksoy Department of Mathematics, Faculty of Science and Letters, Kafkas University, Kars Turkey

Keywords: Quasi optic; Schrodinger equation; optimal control

Abstract

In this paper, the finite difference method is applied to the optimal control problem of system governed by stationary equation of Quasi-Optic . For this aim, 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.

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