An optimal control approach for solving an inverse heat source problem applying shifted Legendre polynomials
This study addresses the inverse issue of identifying the space-dependent heat source of the heat equation, which is stated using the optimal con-trol framework. For the numerical solution of this class of problems, an approach based on shifted Legendre polynomials and the associated oper-ational ma...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Ferdowsi University of Mashhad
2023-09-01
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| Series: | Iranian Journal of Numerical Analysis and Optimization |
| Subjects: | |
| Online Access: | https://ijnao.um.ac.ir/article_43685_1ef940d5e57278e43eeb2e0828c0532d.pdf |
| _version_ | 1797774501915656192 |
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| author | T. Shojaeizadeh M. Darehmiraki |
| author_facet | T. Shojaeizadeh M. Darehmiraki |
| author_sort | T. Shojaeizadeh |
| collection | DOAJ |
| description | This study addresses the inverse issue of identifying the space-dependent heat source of the heat equation, which is stated using the optimal con-trol framework. For the numerical solution of this class of problems, an approach based on shifted Legendre polynomials and the associated oper-ational matrix is presented. The approach turns the primary problem into the solution of a system of nonlinear algebraic equations. To do this, the temperature and heat source variables are enlarged in terms of the shifted Legendre polynomials with unknown coefficients employed in the objectivefunction, inverse problem, and initial and Neumann boundary conditions. When paired with their operational matrix, these basis functions provide a quadratic optimization problem with linear constraints, which is then solved using the Lagrange multipliers approach. To assess the method’s efficacy and precision, two examples are provided. |
| first_indexed | 2024-03-12T22:22:03Z |
| format | Article |
| id | doaj.art-b4b05ed3ca7b42bc85ac226d9a3ed313 |
| institution | Directory Open Access Journal |
| issn | 2423-6977 2423-6969 |
| language | English |
| last_indexed | 2024-03-12T22:22:03Z |
| publishDate | 2023-09-01 |
| publisher | Ferdowsi University of Mashhad |
| record_format | Article |
| series | Iranian Journal of Numerical Analysis and Optimization |
| spelling | doaj.art-b4b05ed3ca7b42bc85ac226d9a3ed3132023-07-23T05:04:02ZengFerdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-69772423-69692023-09-0113346048010.22067/ijnao.2023.81202.122143685An optimal control approach for solving an inverse heat source problem applying shifted Legendre polynomialsT. Shojaeizadeh0M. Darehmiraki1Department of Mathematics, Qom Branch, Islamic Azad University, Qom, Iran.Department of Mathematics, Behbahan Khatam Alanbia University of Technology, Khouzestan, Iran.This study addresses the inverse issue of identifying the space-dependent heat source of the heat equation, which is stated using the optimal con-trol framework. For the numerical solution of this class of problems, an approach based on shifted Legendre polynomials and the associated oper-ational matrix is presented. The approach turns the primary problem into the solution of a system of nonlinear algebraic equations. To do this, the temperature and heat source variables are enlarged in terms of the shifted Legendre polynomials with unknown coefficients employed in the objectivefunction, inverse problem, and initial and Neumann boundary conditions. When paired with their operational matrix, these basis functions provide a quadratic optimization problem with linear constraints, which is then solved using the Lagrange multipliers approach. To assess the method’s efficacy and precision, two examples are provided.https://ijnao.um.ac.ir/article_43685_1ef940d5e57278e43eeb2e0828c0532d.pdfinverse problemsoptimal control problemshifted legendre polynomials (slps)heat sourceoperational matrix |
| spellingShingle | T. Shojaeizadeh M. Darehmiraki An optimal control approach for solving an inverse heat source problem applying shifted Legendre polynomials Iranian Journal of Numerical Analysis and Optimization inverse problems optimal control problem shifted legendre polynomials (slps) heat source operational matrix |
| title | An optimal control approach for solving an inverse heat source problem applying shifted Legendre polynomials |
| title_full | An optimal control approach for solving an inverse heat source problem applying shifted Legendre polynomials |
| title_fullStr | An optimal control approach for solving an inverse heat source problem applying shifted Legendre polynomials |
| title_full_unstemmed | An optimal control approach for solving an inverse heat source problem applying shifted Legendre polynomials |
| title_short | An optimal control approach for solving an inverse heat source problem applying shifted Legendre polynomials |
| title_sort | optimal control approach for solving an inverse heat source problem applying shifted legendre polynomials |
| topic | inverse problems optimal control problem shifted legendre polynomials (slps) heat source operational matrix |
| url | https://ijnao.um.ac.ir/article_43685_1ef940d5e57278e43eeb2e0828c0532d.pdf |
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