Numerical Solution of a Free Boundary Problem from Heat Transfer by the Second Kind Chebyshev Wavelets
In this paper we reduce a free boundary problem from heat transfer to a weakly Singular Volterra integral equation of the first kind. Since the first kind integral equation is ill posed, and an appropriate method for such ill posed problems is based on wavelets, then we apply the Chebyshev wavelets...
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| Language: | English |
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University of Tehran
2019-11-01
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| Series: | Journal of Sciences, Islamic Republic of Iran |
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| Online Access: | https://jsciences.ut.ac.ir/article_73610_496879cb1914862cb20e4b9b96966c43.pdf |
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| author | Bahman Babayar-Razlighi |
| author_facet | Bahman Babayar-Razlighi |
| author_sort | Bahman Babayar-Razlighi |
| collection | DOAJ |
| description | In this paper we reduce a free boundary problem from heat transfer to a weakly Singular Volterra integral equation of the first kind. Since the first kind integral equation is ill posed, and an appropriate method for such ill posed problems is based on wavelets, then we apply the Chebyshev wavelets to solve the integral equation. Numerical implementation of the method is illustrated by two benchmark problems originated from heat transfer. The behavior of the initial and free boundary heat functions along the position axis during the time have been shown through some three dimensional plots. The convergence of the method is pointed in the end of section 2. The numerical examples show the accuracy and applicability of the method from application and programming points of views. |
| format | Article |
| id | doaj-art-e62b33b90e2b4e0ebc0171ba9bb7a77f |
| institution | OA Journals |
| issn | 1016-1104 2345-6914 |
| language | English |
| publishDate | 2019-11-01 |
| publisher | University of Tehran |
| record_format | Article |
| series | Journal of Sciences, Islamic Republic of Iran |
| spelling | doaj-art-e62b33b90e2b4e0ebc0171ba9bb7a77f2025-08-20T01:53:37ZengUniversity of TehranJournal of Sciences, Islamic Republic of Iran1016-11042345-69142019-11-0130435536210.22059/jsciences.2019.279230.100739373610Numerical Solution of a Free Boundary Problem from Heat Transfer by the Second Kind Chebyshev WaveletsBahman Babayar-Razlighi0Department of Mathematics, Faculty of science, Qom University of Technology, Qom, IranIn this paper we reduce a free boundary problem from heat transfer to a weakly Singular Volterra integral equation of the first kind. Since the first kind integral equation is ill posed, and an appropriate method for such ill posed problems is based on wavelets, then we apply the Chebyshev wavelets to solve the integral equation. Numerical implementation of the method is illustrated by two benchmark problems originated from heat transfer. The behavior of the initial and free boundary heat functions along the position axis during the time have been shown through some three dimensional plots. The convergence of the method is pointed in the end of section 2. The numerical examples show the accuracy and applicability of the method from application and programming points of views.https://jsciences.ut.ac.ir/article_73610_496879cb1914862cb20e4b9b96966c43.pdfvolterra integral equation of the first kindheat equationnumerical solutionsecond kind chebyshev waveletsfree boundary |
| spellingShingle | Bahman Babayar-Razlighi Numerical Solution of a Free Boundary Problem from Heat Transfer by the Second Kind Chebyshev Wavelets Journal of Sciences, Islamic Republic of Iran volterra integral equation of the first kind heat equation numerical solution second kind chebyshev wavelets free boundary |
| title | Numerical Solution of a Free Boundary Problem from Heat Transfer by the Second Kind Chebyshev Wavelets |
| title_full | Numerical Solution of a Free Boundary Problem from Heat Transfer by the Second Kind Chebyshev Wavelets |
| title_fullStr | Numerical Solution of a Free Boundary Problem from Heat Transfer by the Second Kind Chebyshev Wavelets |
| title_full_unstemmed | Numerical Solution of a Free Boundary Problem from Heat Transfer by the Second Kind Chebyshev Wavelets |
| title_short | Numerical Solution of a Free Boundary Problem from Heat Transfer by the Second Kind Chebyshev Wavelets |
| title_sort | numerical solution of a free boundary problem from heat transfer by the second kind chebyshev wavelets |
| topic | volterra integral equation of the first kind heat equation numerical solution second kind chebyshev wavelets free boundary |
| url | https://jsciences.ut.ac.ir/article_73610_496879cb1914862cb20e4b9b96966c43.pdf |
| work_keys_str_mv | AT bahmanbabayarrazlighi numericalsolutionofafreeboundaryproblemfromheattransferbythesecondkindchebyshevwavelets |