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Stable numerical solution of an inverse coefficient problem for a time fractional reaction-diffusion equation | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 28، دوره 12، شماره 1، مرداد 2021، صفحه 365-383 اصل مقاله (1.64 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.4810 | ||
| نویسندگان | ||
| Afshin Babaei* 1؛ Seddigheh Banihashemi2؛ Javad Damirchi3 | ||
| 1Department of Mathematics, Faculty of Mathematical sciences, University of Mazandaran, P.O. Box: 47416-95447, Babolsar, Iran. | ||
| 2Department of Applied Mathematics, University of Mazandaran, P.O. Box: 47416-95447, Babolsar, Iran | ||
| 3Department of Mathematics, Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran | ||
| تاریخ دریافت: 19 مهر 1396، تاریخ بازنگری: 05 تیر 1399، تاریخ پذیرش: 26 تیر 1399 | ||
| چکیده | ||
| In this paper, an inverse problem of determining an unknown reaction coefficient in a one-dimensional time-fractional reaction-diffusion equation is considered. This inverse problem is generally ill-posed. For this reason, the mollification regularization technique with the generalized cross-validation criteria will be employed to find an equivalent stable problem. Afterward, a finite difference marching scheme is introduced to solve this regularized problem. The stability and convergence of the numerical solution are investigated. In the end, some numerical examples are presented to verify the ability and effectiveness of the proposed algorithm. | ||
| کلیدواژه‌ها | ||
| Inverse problem؛ Time fractional reaction-diffusion equation؛ Caputo's fractional derivative؛ Mollification؛ Marching scheme | ||
| مراجع | ||
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