Boundary integral equations with the generalized Neumann Kernal for Robin's equation for multiply connected regions
Also available in printed version
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| Format: | Doctoral thesis |
| Language: | English |
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Universiti Teknologi Malaysia
2025
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| Online Access: | https://utmik.utm.my/handle/123456789/51867 |
| Abstract | Abstract here |
| _version_ | 1854975063599611904 |
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| author | Al-Shatri, Shwan Hassan Hussein |
| author2 | Munira Ismail, supervisor |
| author_facet | Munira Ismail, supervisor Al-Shatri, Shwan Hassan Hussein |
| author_sort | Al-Shatri, Shwan Hassan Hussein |
| description | Also available in printed version |
| format | Doctoral thesis |
| id | utm-123456789-51867 |
| institution | Universiti Teknologi Malaysia |
| language | English |
| publishDate | 2025 |
| publisher | Universiti Teknologi Malaysia |
| record_format | dspace |
| record_pdf | Abstract |
| spelling | utm-123456789-518672025-08-20T22:48:23Z Boundary integral equations with the generalized Neumann Kernal for Robin's equation for multiply connected regions Al-Shatri, Shwan Hassan Hussein Munira Ismail, supervisor Science Also available in printed version This research offers an effective boundary integral equation method for seeking numerical solution of the Robin problems on both bounded and unbounded simply and multiply connected regions. A Robin problem consists of finding a harmonic function u in a region satisfying the boundary condition which is a linear combination of Dirichlet and Neumann conditions on the boundary T = an. In this thesis, a Robin problem is reformulated into a Riemann Hilbert problem, which satisfies two integral equations with generalized Neumann kernel. The proof that these integral equations are linearly independent is provided. These integral equations are nonuniquely solvable hence additional conditions are imposed to the Robin problem and are included with the integral equations so that both become uniquely solvable. One of these conditions contains derivatives which are approximated using five point central difference method where appropriate, otherwise the forward or backward difference methods are used. Another condition is obtained from the Cauchy integral formula. When the Riemann Hilbert problem are allowed to satisfy only one integral equation with generalized Neumann kernel, then the normalizing conditions are also imposed besides the other conditions mentioned above. The obtained integral equation with the boundary conditions are discretized by the Nystr¨om method and numerical integrations are by trapezoidal rule while the Wittich’s method is employed to approximate the singular part within the integral equation. The presented numerical results illustrate that the proposed method can be used to produce approximations of high accuracy, for Robin problem on bounded and unbounded simply and multiply connected regions fahmimoksen UTM 298 p. Thesis (Ph.D (Matematik)) - Universiti Teknologi Malaysia, 2016 2025-03-14T06:46:10Z 2025-03-14T06:46:10Z 2016 Doctoral thesis https://utmik.utm.my/handle/123456789/51867 vital:106475 valet-20180103-081557 ENG Closed Access UTM Complete Unpublished Completion application/pdf Universiti Teknologi Malaysia |
| spellingShingle | Science Al-Shatri, Shwan Hassan Hussein Boundary integral equations with the generalized Neumann Kernal for Robin's equation for multiply connected regions |
| thesis_level | PhD |
| title | Boundary integral equations with the generalized Neumann Kernal for Robin's equation for multiply connected regions |
| title_full | Boundary integral equations with the generalized Neumann Kernal for Robin's equation for multiply connected regions |
| title_fullStr | Boundary integral equations with the generalized Neumann Kernal for Robin's equation for multiply connected regions |
| title_full_unstemmed | Boundary integral equations with the generalized Neumann Kernal for Robin's equation for multiply connected regions |
| title_short | Boundary integral equations with the generalized Neumann Kernal for Robin's equation for multiply connected regions |
| title_sort | boundary integral equations with the generalized neumann kernal for robin s equation for multiply connected regions |
| topic | Science |
| url | https://utmik.utm.my/handle/123456789/51867 |
| work_keys_str_mv | AT alshatrishwanhassanhussein boundaryintegralequationswiththegeneralizedneumannkernalforrobinsequationformultiplyconnectedregions |