Email this article Efficient Iterative Method for Solving Optimal Control Problem Governed by Diffusion Equation with Time Fractional Derivative
- Authors: Lapin A.1,2, Laitinen E.3
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Affiliations:
- Institute of Computational Mathematics and Information Technologies
- Coordinated Innovation Center for Computable Modeling in Management Science Tianjin University of Finance and Economics
- Unit of Mathematical Sciences
- Issue: Vol 40, No 4 (2019)
- Pages: 479-488
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/204273
- DOI: https://doi.org/10.1134/S1995080219040103
- ID: 204273
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Abstract
We solve finite-difference approximations of a linear-quadratic optimal control problem governed by Dirichlet boundary value problem with fractional time derivative. The state equation of the problem is approximated using locally one-dimensional difference schemes. The stability estimates of discrete state equations necessary for studying the convergence of iterative solution methods for the constructed discrete optimal control problems are proved. The rate of convergence of the proposed iterative method is obtained and the optimal iterative parameter is found. The results of numerical tests for a model problem are presented.
About the authors
A. Lapin
Institute of Computational Mathematics and Information Technologies; Coordinated Innovation Center for Computable Modeling in Management Science Tianjin University of Finance and Economics
Author for correspondence.
Email: avlapine@mail.ru
Russian Federation, Kazan, Tatarstan, 420008; Tianjin, 300222
E. Laitinen
Unit of Mathematical Sciences
Author for correspondence.
Email: erkki.laitinen@oulu.fi
Finland, Oulu
