One-step block methods for direct solving of linear boundary value Dirichlet and Neumann type problems

In this research, the block methods have been used to solve the second order linear boundary value problems of Dirichlet and Neumann type. Mathematical problems which involve higher order ordinary differential equations were likely to be reduced into the system of first order equations. However, the...

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Main Author:	Hasni, Mohd Mughti
Format:	Thesis
Language:	English
Published:	2014
Subjects:	Boundary value problems Dirichlet problem - Numerical solutions Neumann problem - Numerical solutions
Online Access:	http://psasir.upm.edu.my/id/eprint/76041/1/IPM%202014%2012%20-%20IR.pdf
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id	my-upm-ir.76041
record_format	uketd_dc
spelling	my-upm-ir.760412019-11-26T07:08:27Z One-step block methods for direct solving of linear boundary value Dirichlet and Neumann type problems 2014-02 Hasni, Mohd Mughti In this research, the block methods have been used to solve the second order linear boundary value problems of Dirichlet and Neumann type. Mathematical problems which involve higher order ordinary differential equations were likely to be reduced into the system of first order equations. However, these block methods will solve the problems directly without reducing it into the first order equations using constant step size. There are three methods that have been used in this research which are two point one-step block method, three point one-step block method and four point one-step block method. Each of these methods will be implemented to solve the second order linear boundary value problems with two different types of boundary conditions i.e. Dirichlet and Neumann type. Those three methods will be implemented together with the linear shooting technique to construct the numerical solution. The stability for each method will be presented. Numerical results of the methods are compared with the existing methods. As a conclusion, the proposed block methods can give better and comparable accuracy with the advantage of less costly. Thus, the proposed block methods are suitable to solve the second order linear boundary value problems of Dirichlet and Neumann type directly. Boundary value problems Dirichlet problem - Numerical solutions Neumann problem - Numerical solutions 2014-02 Thesis http://psasir.upm.edu.my/id/eprint/76041/ http://psasir.upm.edu.my/id/eprint/76041/1/IPM%202014%2012%20-%20IR.pdf text en public masters Universiti Putra Malaysia Boundary value problems Dirichlet problem - Numerical solutions Neumann problem - Numerical solutions
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English
topic	Boundary value problems Dirichlet problem - Numerical solutions Neumann problem - Numerical solutions
spellingShingle	Boundary value problems Dirichlet problem - Numerical solutions Neumann problem - Numerical solutions Hasni, Mohd Mughti One-step block methods for direct solving of linear boundary value Dirichlet and Neumann type problems
description	In this research, the block methods have been used to solve the second order linear boundary value problems of Dirichlet and Neumann type. Mathematical problems which involve higher order ordinary differential equations were likely to be reduced into the system of first order equations. However, these block methods will solve the problems directly without reducing it into the first order equations using constant step size. There are three methods that have been used in this research which are two point one-step block method, three point one-step block method and four point one-step block method. Each of these methods will be implemented to solve the second order linear boundary value problems with two different types of boundary conditions i.e. Dirichlet and Neumann type. Those three methods will be implemented together with the linear shooting technique to construct the numerical solution. The stability for each method will be presented. Numerical results of the methods are compared with the existing methods. As a conclusion, the proposed block methods can give better and comparable accuracy with the advantage of less costly. Thus, the proposed block methods are suitable to solve the second order linear boundary value problems of Dirichlet and Neumann type directly.
format	Thesis
qualification_level	Master's degree
author	Hasni, Mohd Mughti
author_facet	Hasni, Mohd Mughti
author_sort	Hasni, Mohd Mughti
title	One-step block methods for direct solving of linear boundary value Dirichlet and Neumann type problems
title_short	One-step block methods for direct solving of linear boundary value Dirichlet and Neumann type problems
title_full	One-step block methods for direct solving of linear boundary value Dirichlet and Neumann type problems
title_fullStr	One-step block methods for direct solving of linear boundary value Dirichlet and Neumann type problems
title_full_unstemmed	One-step block methods for direct solving of linear boundary value Dirichlet and Neumann type problems
title_sort	one-step block methods for direct solving of linear boundary value dirichlet and neumann type problems
granting_institution	Universiti Putra Malaysia
publishDate	2014
url	http://psasir.upm.edu.my/id/eprint/76041/1/IPM%202014%2012%20-%20IR.pdf
_version_	1747813105864278016

One-step block methods for direct solving of linear boundary value Dirichlet and Neumann type problems

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