Noniterative Localized and Space-Time Localized RBF Meshless Method to Solve the Ill-Posed and Inverse Problem
In many references, both the ill-posed and inverse boundary value problems are solved iteratively. The iterative procedures are based on firstly converting the problem into a well-posed one by assuming the missing boundary values. Then, the problem is solved by using either a developed numerical alg...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Modelling and Simulation in Engineering |
| Online Access: | http://dx.doi.org/10.1155/2020/5046286 |
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| author | Mohammed Hamaidi Ahmed Naji Fatima Ghafrani Mostafa Jourhmane |
| author_facet | Mohammed Hamaidi Ahmed Naji Fatima Ghafrani Mostafa Jourhmane |
| author_sort | Mohammed Hamaidi |
| collection | DOAJ |
| description | In many references, both the ill-posed and inverse boundary value problems are solved iteratively. The iterative procedures are based on firstly converting the problem into a well-posed one by assuming the missing boundary values. Then, the problem is solved by using either a developed numerical algorithm or a conventional optimization scheme. The convergence of the technique is achieved when the approximated solution is well compared to the unused data. In the present paper, we present a different way to solve an ill-posed problem by applying the localized and space-time localized radial basis function collocation method depending on the problem considered and avoiding the iterative procedure. We demonstrate that the solution of certain ill-posed and inverse problems can be accomplished without iterations. Three different problems have been investigated: problems with missing boundary condition and internal data, problems with overspecified boundary condition, and backward heat conduction problem (BHCP). It has been demonstrated that the presented method is efficient and accurate and overcomes the stability analysis that is required in iterative techniques. |
| format | Article |
| id | doaj-art-6a75283e0b9c4abbb9377c08d0941454 |
| institution | Kabale University |
| issn | 1687-5591 1687-5605 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Modelling and Simulation in Engineering |
| spelling | doaj-art-6a75283e0b9c4abbb9377c08d09414542025-02-03T06:06:29ZengWileyModelling and Simulation in Engineering1687-55911687-56052020-01-01202010.1155/2020/50462865046286Noniterative Localized and Space-Time Localized RBF Meshless Method to Solve the Ill-Posed and Inverse ProblemMohammed Hamaidi0Ahmed Naji1Fatima Ghafrani2Mostafa Jourhmane3Department of Mathematics, Faculty of Sciences and Techniques, Abdelmalek Essaadi University, Box 416, Tangier, MoroccoDepartment of Mathematics, Faculty of Sciences and Techniques, Abdelmalek Essaadi University, Box 416, Tangier, MoroccoDepartment of Mathematics, Polydisciplinary Faculty of Larache, Abdelmalek Essaadi University, Box 745, Larache, MoroccoDepartment of Mathematics, Faculty of Sciences and Techniques, University of Sultan Moulay Slimane, Box 523, Beni Mellal, MoroccoIn many references, both the ill-posed and inverse boundary value problems are solved iteratively. The iterative procedures are based on firstly converting the problem into a well-posed one by assuming the missing boundary values. Then, the problem is solved by using either a developed numerical algorithm or a conventional optimization scheme. The convergence of the technique is achieved when the approximated solution is well compared to the unused data. In the present paper, we present a different way to solve an ill-posed problem by applying the localized and space-time localized radial basis function collocation method depending on the problem considered and avoiding the iterative procedure. We demonstrate that the solution of certain ill-posed and inverse problems can be accomplished without iterations. Three different problems have been investigated: problems with missing boundary condition and internal data, problems with overspecified boundary condition, and backward heat conduction problem (BHCP). It has been demonstrated that the presented method is efficient and accurate and overcomes the stability analysis that is required in iterative techniques.http://dx.doi.org/10.1155/2020/5046286 |
| spellingShingle | Mohammed Hamaidi Ahmed Naji Fatima Ghafrani Mostafa Jourhmane Noniterative Localized and Space-Time Localized RBF Meshless Method to Solve the Ill-Posed and Inverse Problem Modelling and Simulation in Engineering |
| title | Noniterative Localized and Space-Time Localized RBF Meshless Method to Solve the Ill-Posed and Inverse Problem |
| title_full | Noniterative Localized and Space-Time Localized RBF Meshless Method to Solve the Ill-Posed and Inverse Problem |
| title_fullStr | Noniterative Localized and Space-Time Localized RBF Meshless Method to Solve the Ill-Posed and Inverse Problem |
| title_full_unstemmed | Noniterative Localized and Space-Time Localized RBF Meshless Method to Solve the Ill-Posed and Inverse Problem |
| title_short | Noniterative Localized and Space-Time Localized RBF Meshless Method to Solve the Ill-Posed and Inverse Problem |
| title_sort | noniterative localized and space time localized rbf meshless method to solve the ill posed and inverse problem |
| url | http://dx.doi.org/10.1155/2020/5046286 |
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