Integral equation approach for computing green's function on unbounded simply connected region
This research is to compute the Green’s function on an unbounded simply connected region by conformal mapping and by solving an exterior Dirichlet problem. The exact Green’s function is found by using Riemann mapping and M bius transform. The Dirichlet problem is then solved using a uniquely solvabl...
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| التنسيق: | أطروحة |
| اللغة: | English |
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2013
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| الوصول للمادة أونلاين: | http://eprints.utm.my/id/eprint/47944/25/SheidaChahkandiNezhadMFS2013.pdf |
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my-utm-ep.479442017-07-17T06:48:31Z Integral equation approach for computing green's function on unbounded simply connected region 2013-06 Nezhad, Sheida Chahkandi QA Mathematics This research is to compute the Green’s function on an unbounded simply connected region by conformal mapping and by solving an exterior Dirichlet problem. The exact Green’s function is found by using Riemann mapping and M bius transform. The Dirichlet problem is then solved using a uniquely solvable Fredholm integral equation on the boundary of the region. The kernel of this integral equation is the generalized Neumann kernel. The method for solving this integral equation is by using the Nystr?m method with the trapezoidal rule to discretize it into a system. The linear system is solved by the Gaussian elimination method. As an examination of the proposed method, several numerical examples for some various test regions are presented. These examples include a comparison between the numerical result and the exact solutions. 2013-06 Thesis http://eprints.utm.my/id/eprint/47944/ http://eprints.utm.my/id/eprint/47944/25/SheidaChahkandiNezhadMFS2013.pdf application/pdf en public masters Universiti Teknologi Malaysia, Faculty of Science Faculty of Science |
| institution |
Universiti Teknologi Malaysia |
| collection |
UTM Institutional Repository |
| language |
English |
| topic |
QA Mathematics |
| spellingShingle |
QA Mathematics Nezhad, Sheida Chahkandi Integral equation approach for computing green's function on unbounded simply connected region |
| description |
This research is to compute the Green’s function on an unbounded simply connected region by conformal mapping and by solving an exterior Dirichlet problem. The exact Green’s function is found by using Riemann mapping and M bius transform. The Dirichlet problem is then solved using a uniquely solvable Fredholm integral equation on the boundary of the region. The kernel of this integral equation is the generalized Neumann kernel. The method for solving this integral equation is by using the Nystr?m method with the trapezoidal rule to discretize it into a system. The linear system is solved by the Gaussian elimination method. As an examination of the proposed method, several numerical examples for some various test regions are presented. These examples include a comparison between the numerical result and the exact solutions. |
| format |
Thesis |
| qualification_level |
Master's degree |
| author |
Nezhad, Sheida Chahkandi |
| author_facet |
Nezhad, Sheida Chahkandi |
| author_sort |
Nezhad, Sheida Chahkandi |
| title |
Integral equation approach for computing green's function on unbounded simply connected region |
| title_short |
Integral equation approach for computing green's function on unbounded simply connected region |
| title_full |
Integral equation approach for computing green's function on unbounded simply connected region |
| title_fullStr |
Integral equation approach for computing green's function on unbounded simply connected region |
| title_full_unstemmed |
Integral equation approach for computing green's function on unbounded simply connected region |
| title_sort |
integral equation approach for computing green's function on unbounded simply connected region |
| granting_institution |
Universiti Teknologi Malaysia, Faculty of Science |
| granting_department |
Faculty of Science |
| publishDate |
2013 |
| url |
http://eprints.utm.my/id/eprint/47944/25/SheidaChahkandiNezhadMFS2013.pdf |
| _version_ |
1747817269651570688 |