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.
| Published in | Applied and Computational Mathematics (Volume 4, Issue 2) |
| DOI | 10.11648/j.acm.20150402.11 |
| Page(s) | 30-38 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2024. Published by Science Publishing Group |
Optimal Control, Schrodinger Operator, Finite Difference Methods, Stability, Convergence of Numerical Methods
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APA Style
Fatma Toyoglu, Gabil Yagubov. (2015). Numerical Solution of an Optimal Control Problem Governed by Two Dimensional Schrodinger Equation. Applied and Computational Mathematics, 4(2), 30-38. https://doi.org/10.11648/j.acm.20150402.11
ACS Style
Fatma Toyoglu; Gabil Yagubov. Numerical Solution of an Optimal Control Problem Governed by Two Dimensional Schrodinger Equation. Appl. Comput. Math. 2015, 4(2), 30-38. doi: 10.11648/j.acm.20150402.11
AMA Style
Fatma Toyoglu, Gabil Yagubov. Numerical Solution of an Optimal Control Problem Governed by Two Dimensional Schrodinger Equation. Appl Comput Math. 2015;4(2):30-38. doi: 10.11648/j.acm.20150402.11
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Download@article{10.11648/j.acm.20150402.11,
author = {Fatma Toyoglu and Gabil Yagubov},
title = {Numerical Solution of an Optimal Control Problem Governed by Two Dimensional Schrodinger Equation},
journal = {Applied and Computational Mathematics},
volume = {4},
number = {2},
pages = {30-38},
doi = {10.11648/j.acm.20150402.11},
url = {https://doi.org/10.11648/j.acm.20150402.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20150402.11},
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.},
year = {2015}
}
TY - JOUR T1 - Numerical Solution of an Optimal Control Problem Governed by Two Dimensional Schrodinger Equation AU - Fatma Toyoglu AU - Gabil Yagubov Y1 - 2015/03/04 PY - 2015 N1 - https://doi.org/10.11648/j.acm.20150402.11 DO - 10.11648/j.acm.20150402.11 T2 - Applied and Computational Mathematics JF - Applied and Computational Mathematics JO - Applied and Computational Mathematics SP - 30 EP - 38 PB - Science Publishing Group SN - 2328-5613 UR - https://doi.org/10.11648/j.acm.20150402.11 AB - 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. VL - 4 IS - 2 ER -
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