The Method Based on Series Solution for Identifying an Unknown Source Coefficient on the Temperature Field in the Quasiperiodic Media
In this paper, we consider the reconstruction of heat field in one-dimensional quasiperiodic media with an unknown source from the interior measurement. The innovation of this paper is solving the inverse problem by means of two different homotopy iteration processes. The first kind of homotopy iter...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2021-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2021/2893299 |
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| _version_ | 1832558881145880576 |
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| author | Bingxian Wang Chuanzhi Bai M. Xu L. P. Zhang |
| author_facet | Bingxian Wang Chuanzhi Bai M. Xu L. P. Zhang |
| author_sort | Bingxian Wang |
| collection | DOAJ |
| description | In this paper, we consider the reconstruction of heat field in one-dimensional quasiperiodic media with an unknown source from the interior measurement. The innovation of this paper is solving the inverse problem by means of two different homotopy iteration processes. The first kind of homotopy iteration process is not convergent. For the second kind of homotopy iteration process, a convergent result is proved. Based on the uniqueness of this inverse problem and convergence results of the second kind of homotopy iteration process with exact data, the results of two numerical examples show that the proposed method is efficient, and the error of the inversion solution rt is given. |
| format | Article |
| id | doaj-art-9c0e4cd55ec545a4bd9e5a9288ae8e84 |
| institution | Kabale University |
| issn | 1687-9651 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-9c0e4cd55ec545a4bd9e5a9288ae8e842025-02-03T01:31:27ZengWileyInternational Journal of Differential Equations1687-96512021-01-01202110.1155/2021/2893299The Method Based on Series Solution for Identifying an Unknown Source Coefficient on the Temperature Field in the Quasiperiodic MediaBingxian Wang0Chuanzhi Bai1M. Xu2L. P. Zhang3School of Mathematics and StatisticsSchool of Mathematics and StatisticsSchool of Mathematics and StatisticsSchool of Mathematics and StatisticsIn this paper, we consider the reconstruction of heat field in one-dimensional quasiperiodic media with an unknown source from the interior measurement. The innovation of this paper is solving the inverse problem by means of two different homotopy iteration processes. The first kind of homotopy iteration process is not convergent. For the second kind of homotopy iteration process, a convergent result is proved. Based on the uniqueness of this inverse problem and convergence results of the second kind of homotopy iteration process with exact data, the results of two numerical examples show that the proposed method is efficient, and the error of the inversion solution rt is given.http://dx.doi.org/10.1155/2021/2893299 |
| spellingShingle | Bingxian Wang Chuanzhi Bai M. Xu L. P. Zhang The Method Based on Series Solution for Identifying an Unknown Source Coefficient on the Temperature Field in the Quasiperiodic Media International Journal of Differential Equations |
| title | The Method Based on Series Solution for Identifying an Unknown Source Coefficient on the Temperature Field in the Quasiperiodic Media |
| title_full | The Method Based on Series Solution for Identifying an Unknown Source Coefficient on the Temperature Field in the Quasiperiodic Media |
| title_fullStr | The Method Based on Series Solution for Identifying an Unknown Source Coefficient on the Temperature Field in the Quasiperiodic Media |
| title_full_unstemmed | The Method Based on Series Solution for Identifying an Unknown Source Coefficient on the Temperature Field in the Quasiperiodic Media |
| title_short | The Method Based on Series Solution for Identifying an Unknown Source Coefficient on the Temperature Field in the Quasiperiodic Media |
| title_sort | method based on series solution for identifying an unknown source coefficient on the temperature field in the quasiperiodic media |
| url | http://dx.doi.org/10.1155/2021/2893299 |
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