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Numerical Solution of an Optimal Control Problem Governed by Two Dimensional Schrodinger Equation
Applied and Computational Mathematics
Volume 4, Issue 2, April 2015, Pages: 30-38
Received: Feb. 11, 2015; Accepted: Feb. 26, 2015; Published: Mar. 4, 2015
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Authors
Fatma Toyoglu, Department of Mathematics, Faculty of Art and Science, Erzincan University, Erzincan, Turkey
Gabil Yagubov, Department of Mathematics, Faculty of Art and Science, Erzincan University, Erzincan, Turkey; Department of Mathematics, Faculty of Art and Science, Kafkas University, Kars, Turkey
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Abstract
In this study, the finite difference method is applied to an optimal control problem controlled by two functions which are in the coefficients of two-dimensional Schrodinger equation. Convergence of the finite difference approximation according to the functional is proved. We have used the implicit method for solving the two-dimensional Schrodinger equation. Although the implicit scheme obtained from solution of the system of the linear equations is generally numerically stable and convergent without time-step condition, the solution of considered equation is numerically stable with time-step condition, due to the gradient term.
Keywords
Optimal Control, Schrodinger Operator, Finite Difference Methods, Stability, Convergence of Numerical Methods
To cite this article
Fatma Toyoglu, Gabil Yagubov, Numerical Solution of an Optimal Control Problem Governed by Two Dimensional Schrodinger Equation, Applied and Computational Mathematics. Vol. 4, No. 2, 2015, pp. 30-38. doi: 10.11648/j.acm.20150402.11
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