The system of equations for mixed boundary value problem of partial differential equation with constant coefficient
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| Format: | Thesis |
| Language: | English |
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2018
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| Online Access: | https://ir.upsi.edu.my/detailsg.php?det=4454 |
| Abstract | Abstract here |
| _version_ | 1855625759566069760 |
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| author | Nur Syaza Mohd Yusop |
| author_facet | Nur Syaza Mohd Yusop |
| author_sort | Nur Syaza Mohd Yusop |
| description | |
| format | Thesis |
| id | upsi-4454 |
| institution | Universiti Pendidikan Sultan Idris |
| language | English |
| publishDate | 2018 |
| record_format | sWADAH |
| record_pdf | Restricted |
| spelling | upsi-44542020-02-27 The system of equations for mixed boundary value problem of partial differential equation with constant coefficient 2018 Nur Syaza Mohd Yusop QA Mathematics <p>The aim of this research is to produce the system of equations for three different mixed Boundary Value Problems (BVPs). The potential problem which involves the Laplaces equation on a square shape domain was considered, where the boundary is divided into four sets of linear boundary elements. The Boundary Element Method (BEM) was used to approximate the solutions for BVP. The mixed BVPs were reduced to Boundary Integral Equation (BIEs) by using direct method which were related with Greens second identity representation formula. Then, linear interpolation was used on the discretized elements. The results showed that, there are three system of equations which were obtained. For some cases of mixed BVPs which involves discontinuous fluxes problems yields underdetermined systems. Out of the three problems that being considered, one of three BVPs leads to the underdetermined system of equations. Therefore, the transformation for the underdetermined system to the standard form is necessary for the numerical purposes. The gradient approach method which is widely applies to the Dirichlet problem was considered. This gradient approach method is extended to the underdetermined system of equations obtained from the mixed BVP which subsequently transformed to the standard system. In conclusion, the mixed BVP that involve discontinuous fluxes problem will yield to the underdetermined system of equations that prohibits in solving the system numerically. However, by the gradient approach method, the underdetermined system can be transformed to the standard form and can be solved the system numerically. The study implicates that the procedure used in this studies can be extended to higher dimensional mixed BVPs which involved the discontinuous fluxes problems.</p> 2018 thesis https://ir.upsi.edu.my/detailsg.php?det=4454 https://ir.upsi.edu.my/detailsg.php?det=4454 text eng N/A openAccess Masters Universiti Pendidikan Sultan Idris Fakulti Sains dan Matematik <p>Aliabadi, M.H. &Wen, P.H. (2002). The Boundary Element Method: Applications in</p><p>Solids and Structures (Vol.2). Chichester: Wiley.</p><p></p><p>Ali, A. & Rajakumar, C. (2005). The Boundary Element Method Applications in Sound</p><p>and Vibration. A.A.Balkema, Netherlands.</p><p></p><p>Ang, W.T. (2007). A Beginners Course in Boundary Element Methods. Florida : Boca</p><p>Raton.</p><p></p><p>Atkinson, K.E & Chandler, G. (1990). Boundary Integral Equation Methods</p><p>For Solving Laplace's Equation With Nonlinear Boundary Conditions: The</p><p>Smooth Boundary Case. 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| spellingShingle | QA Mathematics Nur Syaza Mohd Yusop The system of equations for mixed boundary value problem of partial differential equation with constant coefficient |
| thesis_level | Master |
| title | The system of equations for mixed boundary value problem of partial differential equation with constant coefficient |
| title_full | The system of equations for mixed boundary value problem of partial differential equation with constant coefficient |
| title_fullStr | The system of equations for mixed boundary value problem of partial differential equation with constant coefficient |
| title_full_unstemmed | The system of equations for mixed boundary value problem of partial differential equation with constant coefficient |
| title_short | The system of equations for mixed boundary value problem of partial differential equation with constant coefficient |
| title_sort | system of equations for mixed boundary value problem of partial differential equation with constant coefficient |
| topic | QA Mathematics |
| url | https://ir.upsi.edu.my/detailsg.php?det=4454 |
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