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An approximate solution of inverse source problem for the time-fractional diffusion equation | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 12 اردیبهشت 1405 اصل مقاله (1.59 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2026.66665.3137 | ||
| نویسندگان | ||
| Settara Loubna* 1؛ Atmania Rahima2؛ Mehri Allaoua3 | ||
| 1Lamahis Laboratory, Departement of Mathematics, University of 20 August 1955, Skikda , Algeria. | ||
| 2LMA Laboratory, Department of Mathematics, University of Badji Mokhtar Annaba, P.O. Box 12, Annaba 23000, Algeria. | ||
| 3LANOS Laboratory,Department of Mathematics, University of Chadli Bendjedid, El-Tarf 36000, Algeria. | ||
| چکیده | ||
| This paper investigates a one-dimensional inverse source problem associated with a time-fractional diffusion equation subject to Dirichlet boundary conditions. The primary focus is on analysing the differentiability of the source function and reformulating the inverse problem in terms of the invertibility input-output mapping. The novelty of the study lies in the characterization of these mappings under the Caputo derivative. To obtain approximate solutions we employ a finite difference scheme based on the $L1$ method. Numerical simulations demonstrate the accuracy and reliability of the proposed approach. Improving algorithmic efficiency will also be a focus of our future research. | ||
| کلیدواژهها | ||
| Time-fractional diffusion equation؛ Caputo fractional derivative؛ inverse problem؛ finite difference method؛ $L1$ method | ||
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آمار تعداد مشاهده مقاله: 24 تعداد دریافت فایل اصل مقاله: 41 |
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