Direct methods via multiple shooting technique for solving boundary value problems

In this thesis, nonlinear two-point second order boundary value problems (BVPs) are solved using the one-point, two-point block and three-point block direct method. Subsequently, the two-point direct block method is extended to solve third order BVPs. It also elaborates on the computational complexi...

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Main Author:	Phang, Pei See
Format:	Thesis
Language:	English
Published:	2015
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Online Access:	http://psasir.upm.edu.my/id/eprint/65434/1/FS%202015%2041IR.pdf
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id	my-upm-ir.65434
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spelling	my-upm-ir.654342018-09-14T08:20:28Z Direct methods via multiple shooting technique for solving boundary value problems 2015-05 Phang, Pei See In this thesis, nonlinear two-point second order boundary value problems (BVPs) are solved using the one-point, two-point block and three-point block direct method. Subsequently, the two-point direct block method is extended to solve third order BVPs. It also elaborates on the computational complexity, stability analysis, consistency, convergent and the order of the methods. Multiple shooting technique via the three-step iterative method is implemented in order to solve the BVPs. This approach can avoid the sensitive BVPs when choosing the wrong initial guessing value and converge faster compared to the existing method. Variable step size strategy is adapted for solving second order and third order BVPs respectively. Furthermore the variable step size and order strategy is developed to solve second order BVPs directly. Besides that, a two-point direct block method is proposed to solve three applications of BVPs in fluid dynamics. These applications are modelled as third order BVPs and system with combination of third and second order BVPs. Numerical results showed that the performance of the developed methods can obtain better results in terms of maximum error, total step, total function calls and execution time when compared to existing method. In conclusion, the proposed direct block methods in this thesis are appropriate for solving second order and third order nonlinear boundary value problem. 2015-05 Thesis http://psasir.upm.edu.my/id/eprint/65434/ http://psasir.upm.edu.my/id/eprint/65434/1/FS%202015%2041IR.pdf text en public doctoral Universiti Putra Malaysia
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English
topic
spellingShingle	Phang, Pei See Direct methods via multiple shooting technique for solving boundary value problems
description	In this thesis, nonlinear two-point second order boundary value problems (BVPs) are solved using the one-point, two-point block and three-point block direct method. Subsequently, the two-point direct block method is extended to solve third order BVPs. It also elaborates on the computational complexity, stability analysis, consistency, convergent and the order of the methods. Multiple shooting technique via the three-step iterative method is implemented in order to solve the BVPs. This approach can avoid the sensitive BVPs when choosing the wrong initial guessing value and converge faster compared to the existing method. Variable step size strategy is adapted for solving second order and third order BVPs respectively. Furthermore the variable step size and order strategy is developed to solve second order BVPs directly. Besides that, a two-point direct block method is proposed to solve three applications of BVPs in fluid dynamics. These applications are modelled as third order BVPs and system with combination of third and second order BVPs. Numerical results showed that the performance of the developed methods can obtain better results in terms of maximum error, total step, total function calls and execution time when compared to existing method. In conclusion, the proposed direct block methods in this thesis are appropriate for solving second order and third order nonlinear boundary value problem.
format	Thesis
qualification_level	Doctorate
author	Phang, Pei See
author_facet	Phang, Pei See
author_sort	Phang, Pei See
title	Direct methods via multiple shooting technique for solving boundary value problems
title_short	Direct methods via multiple shooting technique for solving boundary value problems
title_full	Direct methods via multiple shooting technique for solving boundary value problems
title_fullStr	Direct methods via multiple shooting technique for solving boundary value problems
title_full_unstemmed	Direct methods via multiple shooting technique for solving boundary value problems
title_sort	direct methods via multiple shooting technique for solving boundary value problems
granting_institution	Universiti Putra Malaysia
publishDate	2015
url	http://psasir.upm.edu.my/id/eprint/65434/1/FS%202015%2041IR.pdf
_version_	1747812337069326336

Direct methods via multiple shooting technique for solving boundary value problems

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