Computing Robin Problem on Unbounded Simply Connected Domain via an Integral Equation with the Generalized Neumann Kernel
A Robin problem is a mixed problem with a linear combination of Dirichlet and Neumann D-N conditions. The aim of this paper are presents a new boundary integral equation BIE method for the solution of unbounded Robin boundary value problem BVP in the simply connected domain. The method show how to r...
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| Format: | Article |
| Language: | English |
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Sulaimani Polytechnic University
2017-08-01
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| Series: | Kurdistan Journal of Applied Research |
| Subjects: | |
| Online Access: | http://kjar.spu.edu.iq/index.php/kjar/article/view/75 |
| _version_ | 1818064601201246208 |
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| author | Shwan H. H. Al-Shatri Karzan Wakil Munira Ismail |
| author_facet | Shwan H. H. Al-Shatri Karzan Wakil Munira Ismail |
| author_sort | Shwan H. H. Al-Shatri |
| collection | DOAJ |
| description | A Robin problem is a mixed problem with a linear combination of Dirichlet and Neumann D-N conditions. The aim of this paper are presents a new boundary integral equation BIE method for the solution of unbounded Robin boundary value problem BVP in the simply connected domain. The method show how to reformulate the Robin boundary value problem BVP as Riemann-Hilbert problem RHP which lead to the system of integral equation, and the related differential equations are also created that give rise to unique solutions. Numerical results on several tests regions by the Nyström method NM with the trapezoidal rule TR are presented to clarify the solution technique for the Robin problem when the boundaries are sufficiently smooth. |
| first_indexed | 2024-12-10T14:38:35Z |
| format | Article |
| id | doaj.art-dd9fb581673745909ba93089d9c05ec3 |
| institution | Directory Open Access Journal |
| issn | 2411-7684 2411-7706 |
| language | English |
| last_indexed | 2024-12-10T14:38:35Z |
| publishDate | 2017-08-01 |
| publisher | Sulaimani Polytechnic University |
| record_format | Article |
| series | Kurdistan Journal of Applied Research |
| spelling | doaj.art-dd9fb581673745909ba93089d9c05ec32022-12-22T01:44:45ZengSulaimani Polytechnic UniversityKurdistan Journal of Applied Research2411-76842411-77062017-08-012312012410.24017/science.2017.3.1075Computing Robin Problem on Unbounded Simply Connected Domain via an Integral Equation with the Generalized Neumann KernelShwan H. H. Al-Shatri0Karzan Wakil1Munira Ismail2Science Department, Institute of Training and Educational Development in Sualiamni-IraqSualimani Polytechnic University-Iraq, University of Human Development-IraqDepartment of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, MalaysiaA Robin problem is a mixed problem with a linear combination of Dirichlet and Neumann D-N conditions. The aim of this paper are presents a new boundary integral equation BIE method for the solution of unbounded Robin boundary value problem BVP in the simply connected domain. The method show how to reformulate the Robin boundary value problem BVP as Riemann-Hilbert problem RHP which lead to the system of integral equation, and the related differential equations are also created that give rise to unique solutions. Numerical results on several tests regions by the Nyström method NM with the trapezoidal rule TR are presented to clarify the solution technique for the Robin problem when the boundaries are sufficiently smooth.http://kjar.spu.edu.iq/index.php/kjar/article/view/75Robin problem, Riemann-Hilbert problem, Integral equation, Generalized Neumann kernel, Simply connected region. |
| spellingShingle | Shwan H. H. Al-Shatri Karzan Wakil Munira Ismail Computing Robin Problem on Unbounded Simply Connected Domain via an Integral Equation with the Generalized Neumann Kernel Kurdistan Journal of Applied Research Robin problem, Riemann-Hilbert problem, Integral equation, Generalized Neumann kernel, Simply connected region. |
| title | Computing Robin Problem on Unbounded Simply Connected Domain via an Integral Equation with the Generalized Neumann Kernel |
| title_full | Computing Robin Problem on Unbounded Simply Connected Domain via an Integral Equation with the Generalized Neumann Kernel |
| title_fullStr | Computing Robin Problem on Unbounded Simply Connected Domain via an Integral Equation with the Generalized Neumann Kernel |
| title_full_unstemmed | Computing Robin Problem on Unbounded Simply Connected Domain via an Integral Equation with the Generalized Neumann Kernel |
| title_short | Computing Robin Problem on Unbounded Simply Connected Domain via an Integral Equation with the Generalized Neumann Kernel |
| title_sort | computing robin problem on unbounded simply connected domain via an integral equation with the generalized neumann kernel |
| topic | Robin problem, Riemann-Hilbert problem, Integral equation, Generalized Neumann kernel, Simply connected region. |
| url | http://kjar.spu.edu.iq/index.php/kjar/article/view/75 |
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