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An inverse problem of finding an absorption coefficient in a one-dimensional parabolic differential equation | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 20 فروردین 1405 اصل مقاله (2.07 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2026.64614.2931 | ||
| نویسندگان | ||
| Kamal Rashedi* 1؛ Maryam Ghorbani2 | ||
| 1Department of Mathematics, Faculty of Science, University of Kurdistan, Sanandaj, Iran. | ||
| 2Department of Mathematics, University of Science and Technology of Mazandaran, Behshahr, Iran. | ||
| چکیده | ||
| This paper addresses an inverse problem related to the one-dimensional heat equation, incorporating the initial temperature and information from the heat flux and temperature on one of the boundaries of the domain and a supplementary temperature measurement at an instant of time. To tackle this problem, we utilize a discretization method, introducing approximations for both the temperature distribution and absorption coeffcient functions. These approximations are established using Legendre basis functions and the operational matrix of differentiation corresponding to the selected bases. Subsequently, these estimations are incorporated into the residual function and then the least squares technique is applied to transform the main problem into the solution of a nonlinear system of algebraic equations. Notably, our proposed algorithm ensures accurate satisfaction of the given initial and boundary conditions of the problem. We provide proof of the method’s convergence and showcase its effectiveness through illustrative test examples. | ||
| کلیدواژهها | ||
| Inverse heat equation؛ least squares technique؛ absorption coefficient | ||
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آمار تعداد مشاهده مقاله: 31 تعداد دریافت فایل اصل مقاله: 37 |
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