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Regularization of a nonlinear inverse problem by discrete mollification method | ||
| Computational Methods for Differential Equations | ||
| مقاله 20، دوره 9، شماره 1، فروردین 2021، صفحه 313-326 اصل مقاله (1.25 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2020.30808.1461 | ||
| نویسندگان | ||
| Soheila Bodaghi1؛ Ali Zakeri* 1؛ Amir Amiraslani2 | ||
| 1Faculty of Mathematics, K. N. Toosi University of Technology, Tehran, Iran. | ||
| 2STEM department, University of Hawaii-Maui college | ||
| چکیده | ||
| In this article, the application of discrete mollification as a regularization procedure for solving a nonlinear inverse problem in one dimensional space is considered. Illposedness is identified as one of the main characteristics of inverse problems. It is clear that if we have a noisy data, the inverse problem becomes unstable. As such, a numerical procedure based on discrete mollification and space marching method is applied to address the ill-posedness of the mentioned problem. The regularization parameter is selected by generalized cross validation (GCV) method. The numerical stability and convergence of the proposed method are investigated. Finally, some test problems, whose exact solutions are known, are solved using this method to show the efficiency. | ||
| کلیدواژهها | ||
| Nonlinear inverse problem؛ Discrete mollification؛ Space marching؛ Stability؛ Convergence | ||
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