An integral equation method for solving exterior Neumann problems on smooth regions
This work develops a boundary integral equation method for numerical solution of the exterior Neumann problem. An integral equation for solving the exterior Neumann problem in a simply connected region is derived in this dissertation based on the exterior Riemann-Hilbert problem. In the first step t...
محفوظ في:
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| التنسيق: | أطروحة |
| اللغة: | English |
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2009
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| الوصول للمادة أونلاين: | http://eprints.utm.my/id/eprint/12322/6/AzlinaJumadiMFS2009.pdf |
| الوسوم: |
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my-utm-ep.123222017-09-17T05:37:33Z An integral equation method for solving exterior Neumann problems on smooth regions 2009-11 Jumadi, Azlina Q Science (General) QA Mathematics This work develops a boundary integral equation method for numerical solution of the exterior Neumann problem. An integral equation for solving the exterior Neumann problem in a simply connected region is derived in this dissertation based on the exterior Riemann-Hilbert problem. In the first step the exterior Neumann problem is reduced to an exterior Riemann-Hilbert problem for the derivative of an auxiliary function which is analytic in the region. Then, the exterior Riemann-Hilbert 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 exterior Neumann problem can be obtained. The efficiency of the method is illustrated by some numerical examples. 2009-11 Thesis http://eprints.utm.my/id/eprint/12322/ http://eprints.utm.my/id/eprint/12322/6/AzlinaJumadiMFS2009.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 |
Q Science (General) QA Mathematics |
| spellingShingle |
Q Science (General) QA Mathematics Jumadi, Azlina An integral equation method for solving exterior Neumann problems on smooth regions |
| description |
This work develops a boundary integral equation method for numerical solution of the exterior Neumann problem. An integral equation for solving the exterior Neumann problem in a simply connected region is derived in this dissertation based on the exterior Riemann-Hilbert problem. In the first step the exterior Neumann problem is reduced to an exterior Riemann-Hilbert problem for the derivative of an auxiliary function which is analytic in the region. Then, the exterior Riemann-Hilbert 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 exterior Neumann problem can be obtained. The efficiency of the method is illustrated by some numerical examples. |
| format |
Thesis |
| qualification_level |
Master's degree |
| author |
Jumadi, Azlina |
| author_facet |
Jumadi, Azlina |
| author_sort |
Jumadi, Azlina |
| title |
An integral equation method for solving exterior Neumann problems on smooth regions |
| title_short |
An integral equation method for solving exterior Neumann problems on smooth regions |
| title_full |
An integral equation method for solving exterior Neumann problems on smooth regions |
| title_fullStr |
An integral equation method for solving exterior Neumann problems on smooth regions |
| title_full_unstemmed |
An integral equation method for solving exterior Neumann problems on smooth regions |
| title_sort |
integral equation method for solving exterior neumann problems on smooth regions |
| granting_institution |
Universiti Teknologi Malaysia, Faculty of Science |
| granting_department |
Faculty of Science |
| publishDate |
2009 |
| url |
http://eprints.utm.my/id/eprint/12322/6/AzlinaJumadiMFS2009.pdf |
| _version_ |
1747814923139809280 |