Numerical solution of second order linear two-point boundry value problem using direct multistep method

In this thesis, direct multistep methods are developed for solving second order linear two-point boundary value problems. The proposed direct multistep methods consist of one point direct method and two point direct block method. These methods are then used together with linear shooting technique in...

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Main Author:	Chew, Khui Tat
Format:	Thesis
Language:	English
Published:	2012
Subjects:	Boundary value problems - Numerical solutions
Online Access:	http://psasir.upm.edu.my/id/eprint/38502/7/FS%202012%2088%20IR.pdf
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id	my-upm-ir.38502
record_format	uketd_dc
spelling	my-upm-ir.385022015-07-31T01:45:51Z Numerical solution of second order linear two-point boundry value problem using direct multistep method 2012-11 Chew, Khui Tat In this thesis, direct multistep methods are developed for solving second order linear two-point boundary value problems. The proposed direct multistep methods consist of one point direct method and two point direct block method. These methods are then used together with linear shooting technique in solving second order linear two-point boundary value problems using constant step size. Most of the existing research involving second order linear two-point boundary value problems will reduce the problems to a system of first order ordinary differential equation. This approach will enlarge the system of first order ordinary differential equation and needs more computation work. The advantage of direct multistep methods proposed in this thesis solve second order linear two-point boundary value problems directly without reducing it to first order ordinary differential equation. Moreover, the direct multistep methods are also implemented to solve linear boundary value problems with singular perturbation. The algorithms for solving second order linear two-point boundary value problems and linear boundary value problems with singular perturbation are then executed in programing code which is written in C language. The numerical results showed that the performance of the developed methods gave good results in terms of maximum error and execution time. In conclusion, the proposed methods in this thesis are suitable for solving second order linear two-point boundary value problems and linear boundary value problems with singular perturbation. Boundary value problems - Numerical solutions 2012-11 Thesis http://psasir.upm.edu.my/id/eprint/38502/ http://psasir.upm.edu.my/id/eprint/38502/7/FS%202012%2088%20IR.pdf application/pdf en public masters Universiti Putra Malaysia Boundary value problems - Numerical solutions
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English
topic	Boundary value problems - Numerical solutions
spellingShingle	Boundary value problems - Numerical solutions Chew, Khui Tat Numerical solution of second order linear two-point boundry value problem using direct multistep method
description	In this thesis, direct multistep methods are developed for solving second order linear two-point boundary value problems. The proposed direct multistep methods consist of one point direct method and two point direct block method. These methods are then used together with linear shooting technique in solving second order linear two-point boundary value problems using constant step size. Most of the existing research involving second order linear two-point boundary value problems will reduce the problems to a system of first order ordinary differential equation. This approach will enlarge the system of first order ordinary differential equation and needs more computation work. The advantage of direct multistep methods proposed in this thesis solve second order linear two-point boundary value problems directly without reducing it to first order ordinary differential equation. Moreover, the direct multistep methods are also implemented to solve linear boundary value problems with singular perturbation. The algorithms for solving second order linear two-point boundary value problems and linear boundary value problems with singular perturbation are then executed in programing code which is written in C language. The numerical results showed that the performance of the developed methods gave good results in terms of maximum error and execution time. In conclusion, the proposed methods in this thesis are suitable for solving second order linear two-point boundary value problems and linear boundary value problems with singular perturbation.
format	Thesis
qualification_level	Master's degree
author	Chew, Khui Tat
author_facet	Chew, Khui Tat
author_sort	Chew, Khui Tat
title	Numerical solution of second order linear two-point boundry value problem using direct multistep method
title_short	Numerical solution of second order linear two-point boundry value problem using direct multistep method
title_full	Numerical solution of second order linear two-point boundry value problem using direct multistep method
title_fullStr	Numerical solution of second order linear two-point boundry value problem using direct multistep method
title_full_unstemmed	Numerical solution of second order linear two-point boundry value problem using direct multistep method
title_sort	numerical solution of second order linear two-point boundry value problem using direct multistep method
granting_institution	Universiti Putra Malaysia
publishDate	2012
url	http://psasir.upm.edu.my/id/eprint/38502/7/FS%202012%2088%20IR.pdf
_version_	1747811722855448576

Numerical solution of second order linear two-point boundry value problem using direct multistep method

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