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Source : International Journa ... ✕Department : Uygulamalı Matematik ... ✕
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The solvability of the optimal control problem for a nonlinear Schrödinger equation

Ercan ÇELİK

In this paper, we analyze the solvability of the optimal control problem for a nonlinear Schrodinger equation. A Lions-type functional is considered as the objective functional. First, it is shown that the optimal control problem has at least one solution. Later, the Frechet differentiability of the objective functional is proved and a formula is obtained for its gradient. Finally, a necessary optimality condition is derived. Keywords: frechet differentiability; optimal control problem; optimality conditions; schrödinger equation

Article 2023 Fen Fakültesi International Journal of Optimization and Control: Theories & Applications13 ( 2 ) 24 Views
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An approximate solution of singularly perturbed problem on uniform mesh

Ercan ÇELİK

In this study, we obtain approximate solution for singularly perturbed problem of differential equation having two integral boundary conditions. With this purpose, we propose a new finite difference scheme. First, we construct this exponentially difference scheme on a uniform mesh using the finite difference method. We use the quasilinearization method and the interpolating quadrature formulas to establish the numerical scheme. Then, as a result of the error analysis, we show that the method under study is convergent in the first order. Consequently, theoretical findings are supported by numer ...More

Article 2024 Fen Fakültesi International Journal of Optimization and Control: Theories & Applications14 ( 1 ) 2 Views
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