A collocation method for Fredholm integral equations of the first kind via iterative regularization scheme
To solve the ill-posed integral equations, we use the regularized collocation method. This numerical method is a combination of the Legendre polynomials with non-stationary iterated Tikhonov regularization with fixed parameter. A theoretical justification of the proposed method under the required a...
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| Format: | Article |
| Language: | English |
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Vilnius Gediminas Technical University
2023-03-01
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| Series: | Mathematical Modelling and Analysis |
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| Online Access: | https://limes.vgtu.lt/index.php/MMA/article/view/16453 |
| _version_ | 1827985872286384128 |
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| author | Tahar Bechouat |
| author_facet | Tahar Bechouat |
| author_sort | Tahar Bechouat |
| collection | DOAJ |
| description |
To solve the ill-posed integral equations, we use the regularized collocation method. This numerical method is a combination of the Legendre polynomials with non-stationary iterated Tikhonov regularization with fixed parameter. A theoretical justification of the proposed method under the required assumptions is detailed. Finally, numerical experiments demonstrate the efficiency of this method.
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| first_indexed | 2024-04-09T23:22:33Z |
| format | Article |
| id | doaj.art-ff5fda0d71ad47dea37b961a8703a33a |
| institution | Directory Open Access Journal |
| issn | 1392-6292 1648-3510 |
| language | English |
| last_indexed | 2024-04-09T23:22:33Z |
| publishDate | 2023-03-01 |
| publisher | Vilnius Gediminas Technical University |
| record_format | Article |
| series | Mathematical Modelling and Analysis |
| spelling | doaj.art-ff5fda0d71ad47dea37b961a8703a33a2023-03-21T16:16:51ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102023-03-0128210.3846/mma.2023.16453A collocation method for Fredholm integral equations of the first kind via iterative regularization schemeTahar Bechouat0Faculty of Science and Technology, Department of Mathematics and Informatics, Mohammed Cherif Messaadia University, B.P. 1553 Souk Ahras, 41000 Algeria To solve the ill-posed integral equations, we use the regularized collocation method. This numerical method is a combination of the Legendre polynomials with non-stationary iterated Tikhonov regularization with fixed parameter. A theoretical justification of the proposed method under the required assumptions is detailed. Finally, numerical experiments demonstrate the efficiency of this method. https://limes.vgtu.lt/index.php/MMA/article/view/16453ill-posed problemsiterative regularization schemeLegendre collocation methodintegral equations of the first kind |
| spellingShingle | Tahar Bechouat A collocation method for Fredholm integral equations of the first kind via iterative regularization scheme Mathematical Modelling and Analysis ill-posed problems iterative regularization scheme Legendre collocation method integral equations of the first kind |
| title | A collocation method for Fredholm integral equations of the first kind via iterative regularization scheme |
| title_full | A collocation method for Fredholm integral equations of the first kind via iterative regularization scheme |
| title_fullStr | A collocation method for Fredholm integral equations of the first kind via iterative regularization scheme |
| title_full_unstemmed | A collocation method for Fredholm integral equations of the first kind via iterative regularization scheme |
| title_short | A collocation method for Fredholm integral equations of the first kind via iterative regularization scheme |
| title_sort | collocation method for fredholm integral equations of the first kind via iterative regularization scheme |
| topic | ill-posed problems iterative regularization scheme Legendre collocation method integral equations of the first kind |
| url | https://limes.vgtu.lt/index.php/MMA/article/view/16453 |
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