Huntul, MJ and Lesnic, D orcid.org/0000-0003-3025-2770 (2020) Determination of time-dependent coefficients for a weakly degenerate heat equation. CMES Computer Modeling in Engineering and Sciences, 123 (2). pp. 475-494. ISSN 1526-1492
Abstract
In this paper, we consider solving numerically for the first time inverse problems of determining the time-dependent thermal diffusivity coefficient for a weakly degenerate heat equation, which vanishes at the initial moment of time, and/or the convection coefficient along with the temperature for a one-dimensional parabolic equation, from some additional information about the process (the so-called over-determination conditions). Although uniquely solvable these inverse problems are still ill-posed since small changes in the input data can result in enormous changes in the output solution. The finite difference method with the Crank-Nicolson scheme combined with the nonlinear Tikhonov regularization are employed. The resulting minimization problem is computationally solved using the MATLAB toolbox routine lsqnonlin. For both exact and noisy input data, accurate and stable numerical results are obtained.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | This article is protected by copyright. This is an open access article under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits unrestricted use, distribution and reproduction in any medium, provided the original work is properly cited. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. |
Keywords: | Inverse problem, weakly degenerate heat equation, Tikhonov’s regularization |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 19 Mar 2020 12:14 |
Last Modified: | 25 Jun 2023 22:12 |
Status: | Published |
Publisher: | Tech Science Press |
Identification Number: | 10.32604/cmes.2020.08791 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:158508 |
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