The system of equations for mixed boundary value problem of partial differential equation with constant coefficient (IR)

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 Laplace’s equation on a square shape domain was considered, where the boundary is divided into four sets of linear boundary elem...

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主要作者: Nur Syaza Mohd Yusop
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語言:eng
出版: 2018
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spelling oai:ir.upsi.edu.my:47492020-02-27 The system of equations for mixed boundary value problem of partial differential equation with constant coefficient (IR) 2018 Nur Syaza Mohd Yusop QA Mathematics 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 Laplace’s 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 Green’s 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. 2018 thesis https://ir.upsi.edu.my/detailsg.php?det=4749 https://ir.upsi.edu.my/detailsg.php?det=4749 text eng closedAccess Masters Universiti Pendidikan Sultan Idris Fakulti Sains dan Matematik N/A
institution Universiti Pendidikan Sultan Idris
collection UPSI Digital Repository
language eng
topic QA Mathematics
spellingShingle QA Mathematics
Nur Syaza Mohd Yusop
The system of equations for mixed boundary value problem of partial differential equation with constant coefficient (IR)
description 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 Laplace’s 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 Green’s 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.
format thesis
qualification_name
qualification_level Master's degree
author Nur Syaza Mohd Yusop
author_facet Nur Syaza Mohd Yusop
author_sort Nur Syaza Mohd Yusop
title The system of equations for mixed boundary value problem of partial differential equation with constant coefficient (IR)
title_short The system of equations for mixed boundary value problem of partial differential equation with constant coefficient (IR)
title_full The system of equations for mixed boundary value problem of partial differential equation with constant coefficient (IR)
title_fullStr The system of equations for mixed boundary value problem of partial differential equation with constant coefficient (IR)
title_full_unstemmed The system of equations for mixed boundary value problem of partial differential equation with constant coefficient (IR)
title_sort system of equations for mixed boundary value problem of partial differential equation with constant coefficient (ir)
granting_institution Universiti Pendidikan Sultan Idris
granting_department Fakulti Sains dan Matematik
publishDate 2018
url https://ir.upsi.edu.my/detailsg.php?det=4749
_version_ 1747833144368693248