An integral equation method for solving neumann problems in simply connected regions with smooth boundaries
This paper presents a new method for solving the interior Neumann problem in a simply connected region. The method is based on recent investigations on the interplay of Riemann-Hilbert (RH) problems and Fredholm integral equations with generalized Neumann kernel. In the first step the Neumann proble...
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| Format: | Book Section |
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Faculty of Science, Universiti Teknologi Malaysia
2009
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| Online Access: | http://eprints.utm.my/9029/ |
| _version_ | 1848891794385797120 |
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| author | M. Murid, Ali H. Husin, Ummu Tasnim Rahmat, Hamisan |
| author_facet | M. Murid, Ali H. Husin, Ummu Tasnim Rahmat, Hamisan |
| author_sort | M. Murid, Ali H. |
| building | UTeM Institutional Repository |
| collection | Online Access |
| description | This paper presents a new method for solving the interior Neumann problem in a simply connected region. The method is based on recent investigations on the interplay of Riemann-Hilbert (RH) problems and Fredholm integral equations with generalized Neumann kernel. In the first step the Neumann problem is reformulated as a uniquely solvable interior RH problem for the derivative of an auxiliary function which is analytic in the region. In the second step, the RH problem is transformed to a uniquely solvable Fredholm integral equation on the boundary of the region. Once this equation is solved, the auxiliary function and the solution of the Neumann problem can be obtained. The efficiency of the method is illustrated by some numerical examples. |
| first_indexed | 2025-11-15T21:03:38Z |
| format | Book Section |
| id | utm-9029 |
| institution | Universiti Teknologi Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-15T21:03:38Z |
| publishDate | 2009 |
| publisher | Faculty of Science, Universiti Teknologi Malaysia |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | utm-90292017-09-14T06:19:09Z http://eprints.utm.my/9029/ An integral equation method for solving neumann problems in simply connected regions with smooth boundaries M. Murid, Ali H. Husin, Ummu Tasnim Rahmat, Hamisan Q Science (General) This paper presents a new method for solving the interior Neumann problem in a simply connected region. The method is based on recent investigations on the interplay of Riemann-Hilbert (RH) problems and Fredholm integral equations with generalized Neumann kernel. In the first step the Neumann problem is reformulated as a uniquely solvable interior RH problem for the derivative of an auxiliary function which is analytic in the region. In the second step, the RH problem is transformed to a uniquely solvable Fredholm integral equation on the boundary of the region. Once this equation is solved, the auxiliary function and the solution of the Neumann problem can be obtained. The efficiency of the method is illustrated by some numerical examples. Faculty of Science, Universiti Teknologi Malaysia 2009-05 Book Section PeerReviewed M. Murid, Ali H. and Husin, Ummu Tasnim and Rahmat, Hamisan (2009) An integral equation method for solving neumann problems in simply connected regions with smooth boundaries. In: Proceedings of Second International Conference and Workshops on Basic and Applied Sciences & Regional Annual Fundamental Science Seminar 2009. Faculty of Science, Universiti Teknologi Malaysia. |
| spellingShingle | Q Science (General) M. Murid, Ali H. Husin, Ummu Tasnim Rahmat, Hamisan An integral equation method for solving neumann problems in simply connected regions with smooth boundaries |
| title | An integral equation method for solving neumann problems in simply connected regions with smooth boundaries |
| title_full | An integral equation method for solving neumann problems in simply connected regions with smooth boundaries |
| title_fullStr | An integral equation method for solving neumann problems in simply connected regions with smooth boundaries |
| title_full_unstemmed | An integral equation method for solving neumann problems in simply connected regions with smooth boundaries |
| title_short | An integral equation method for solving neumann problems in simply connected regions with smooth boundaries |
| title_sort | integral equation method for solving neumann problems in simply connected regions with smooth boundaries |
| topic | Q Science (General) |
| url | http://eprints.utm.my/9029/ |