The approximation of the solution of heat conduction problem in circular plate with concentrated initial heat
The approximation of the solution of the heat equation by using the spectral decompositions of the distributions on circular region where initially heat source concentrated at a point is studied. A solution of the problem represented as the Fourier Bessel series that will be understood in terms of...
| Main Authors: | , , |
|---|---|
| Format: | Conference or Workshop Item |
| Language: | English |
| Published: |
AIP Publishing
2024
|
| Subjects: | |
| Online Access: | http://umpir.ump.edu.my/id/eprint/43665/1/p3_2024%20Abdulkasim%20ICOAIMS22%20AIP%20RDU223203.pdf |
| _version_ | 1824451766818701312 |
|---|---|
| author | Akhmedov, Abdulkasim Mohd Zuki, Salleh Rakhimov, Abdumalik |
| author_facet | Akhmedov, Abdulkasim Mohd Zuki, Salleh Rakhimov, Abdumalik |
| author_sort | Akhmedov, Abdulkasim |
| collection | UMP |
| description | The approximation of the solution of the heat equation by using the spectral decompositions of the distributions on
circular region where initially heat source concentrated at a point is studied. A solution of the problem represented as the Fourier Bessel series that will be understood in terms of distributions. Regularized solutions for different values of the order of Riesz means at a singular point are analysed. The numerical approximation of the solution of heat equations on the circular plate with the singular initial heat source is carried out with the help of MATLAB software. The optimization of the regularization of the series solutions at a non-singular point of the plates at initial time and critical index is established, which guaranteed to achieve the good convergence of the Riesz means at the index exceeding a critical point. |
| first_indexed | 2025-02-19T02:39:51Z |
| format | Conference or Workshop Item |
| id | UMPir43665 |
| institution | Universiti Malaysia Pahang |
| language | English |
| last_indexed | 2025-02-19T02:39:51Z |
| publishDate | 2024 |
| publisher | AIP Publishing |
| record_format | dspace |
| spelling | UMPir436652025-01-22T07:24:22Z http://umpir.ump.edu.my/id/eprint/43665/ The approximation of the solution of heat conduction problem in circular plate with concentrated initial heat Akhmedov, Abdulkasim Mohd Zuki, Salleh Rakhimov, Abdumalik QA Mathematics The approximation of the solution of the heat equation by using the spectral decompositions of the distributions on circular region where initially heat source concentrated at a point is studied. A solution of the problem represented as the Fourier Bessel series that will be understood in terms of distributions. Regularized solutions for different values of the order of Riesz means at a singular point are analysed. The numerical approximation of the solution of heat equations on the circular plate with the singular initial heat source is carried out with the help of MATLAB software. The optimization of the regularization of the series solutions at a non-singular point of the plates at initial time and critical index is established, which guaranteed to achieve the good convergence of the Riesz means at the index exceeding a critical point. AIP Publishing 2024-03-07 Conference or Workshop Item PeerReviewed pdf en http://umpir.ump.edu.my/id/eprint/43665/1/p3_2024%20Abdulkasim%20ICOAIMS22%20AIP%20RDU223203.pdf Akhmedov, Abdulkasim and Mohd Zuki, Salleh and Rakhimov, Abdumalik (2024) The approximation of the solution of heat conduction problem in circular plate with concentrated initial heat. In: AIP Conference Proceedings. AIP Conference Proceedings; 3rd International Conference on Applied and Industrial Mathematics and Statistics 2022, ICoAIMS 2022 , 24 - 26 August 2022 , Virtual, Online. pp. 1-7., 2895 (020008). ISSN 0094-243X (Published) https://doi.org/10.1063/5.0193980 https://doi.org/10.1063/5.0193980 |
| spellingShingle | QA Mathematics Akhmedov, Abdulkasim Mohd Zuki, Salleh Rakhimov, Abdumalik The approximation of the solution of heat conduction problem in circular plate with concentrated initial heat |
| title | The approximation of the solution of heat conduction problem in circular plate with concentrated initial heat |
| title_full | The approximation of the solution of heat conduction problem in circular plate with concentrated initial heat |
| title_fullStr | The approximation of the solution of heat conduction problem in circular plate with concentrated initial heat |
| title_full_unstemmed | The approximation of the solution of heat conduction problem in circular plate with concentrated initial heat |
| title_short | The approximation of the solution of heat conduction problem in circular plate with concentrated initial heat |
| title_sort | approximation of the solution of heat conduction problem in circular plate with concentrated initial heat |
| topic | QA Mathematics |
| url | http://umpir.ump.edu.my/id/eprint/43665/1/p3_2024%20Abdulkasim%20ICOAIMS22%20AIP%20RDU223203.pdf |
| work_keys_str_mv | AT akhmedovabdulkasim theapproximationofthesolutionofheatconductionproblemincircularplatewithconcentratedinitialheat AT mohdzukisalleh theapproximationofthesolutionofheatconductionproblemincircularplatewithconcentratedinitialheat AT rakhimovabdumalik theapproximationofthesolutionofheatconductionproblemincircularplatewithconcentratedinitialheat AT akhmedovabdulkasim approximationofthesolutionofheatconductionproblemincircularplatewithconcentratedinitialheat AT mohdzukisalleh approximationofthesolutionofheatconductionproblemincircularplatewithconcentratedinitialheat AT rakhimovabdumalik approximationofthesolutionofheatconductionproblemincircularplatewithconcentratedinitialheat |