Approximation of a Leading Coefficient in an Inverse Heat Conduction Problem via the Ritz Method
This paper presents a numerical approach for reconstructing the leading coefficient in an inverse heat conduction problem (IHCP). We consider a one-dimensional heat equation with known input data, including the initial condition, a supplementary temperature measurement at the final time, an...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Kashan
2025-06-01
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| Series: | Mathematics Interdisciplinary Research |
| Subjects: | |
| Online Access: | https://mir.kashanu.ac.ir/article_114910_55ba5850d43fcadb991c9eaeb8ad7d2b.pdf |
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| Summary: | This paper presents a numerical approach for reconstructing the leading coefficient in an inverse heat conduction problem (IHCP). We consider a one-dimensional heat equation with known input data, including the initial condition, a supplementary temperature measurement at the final time, and two integral observations. By incorporating the terminal condition, the unknown spatially dependent coefficient is eliminated, reducing the problem to a nonclassical parabolic equation. The unknown temperature distribution and its derivatives are approximated and applied to the modified governing equation, which is then discretized using operational matrices of differentiation. To ensure stable derivative estimation, the method is coupled with a regularization technique. A least squares scheme is employed to formulate a nonlinear system of algebraic equations, which is solved using Newton’s method. The reliability of the proposed solution is demonstrated through several numerical examples. |
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| ISSN: | 2476-4965 |