Solving second order boundary value problem by shooting technique using backward difference formulae

In this thesis, the direct implicit multistep method presented in the form of backward difference formula are developed for solving directly two point boundary value problems (BVPs). This method will solve the nonlinear second order BVPs by shooting technique using constant and variable step size. N...

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Main Author:	Jafri, Mahanum Diana
Format:	Thesis
Language:	English
Published:	2011
Subjects:	Boundary value problems Boundary value problems - Numerical solutions Differential equations
Online Access:	http://psasir.upm.edu.my/id/eprint/26514/1/IPM%202011%2020R.pdf
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id	my-upm-ir.26514
record_format	uketd_dc
spelling	my-upm-ir.265142014-11-28T08:02:17Z Solving second order boundary value problem by shooting technique using backward difference formulae 2011-11 Jafri, Mahanum Diana In this thesis, the direct implicit multistep method presented in the form of backward difference formula are developed for solving directly two point boundary value problems (BVPs). This method will solve the nonlinear second order BVPs by shooting technique using constant and variable step size. Newton’s method is considered as a procedure for solving the nonlinear equations and the convergence of the shooting technique. Most of the existing researches involved BVPs will reduce the problem to a system of first order ordinary differential equations (ODEs). This approach is very well established but it obviously will enlarge the system of first order equations. However, the direct multistep method in this thesis will be utilized to obtain series solutions of the initial value problems directly without reducing to first order equations. The coefficients of the developed method will be stored in the code in the form of backward difference formula. The codes were executed in UNIX operating system and the algorithms were written in C language. The numerical results showed that the performance of the developed method is acceptable in terms of maximum error and number of iterations when solving second order nonlinear boundary value problem Boundary value problems Boundary value problems - Numerical solutions Differential equations 2011-11 Thesis http://psasir.upm.edu.my/id/eprint/26514/ http://psasir.upm.edu.my/id/eprint/26514/1/IPM%202011%2020R.pdf application/pdf en public masters Universiti Putra Malaysia Boundary value problems Boundary value problems - Numerical solutions Differential equations Institute for Mathematical Research
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English
topic	Boundary value problems Boundary value problems - Numerical solutions Differential equations
spellingShingle	Boundary value problems Boundary value problems - Numerical solutions Differential equations Jafri, Mahanum Diana Solving second order boundary value problem by shooting technique using backward difference formulae
description	In this thesis, the direct implicit multistep method presented in the form of backward difference formula are developed for solving directly two point boundary value problems (BVPs). This method will solve the nonlinear second order BVPs by shooting technique using constant and variable step size. Newton’s method is considered as a procedure for solving the nonlinear equations and the convergence of the shooting technique. Most of the existing researches involved BVPs will reduce the problem to a system of first order ordinary differential equations (ODEs). This approach is very well established but it obviously will enlarge the system of first order equations. However, the direct multistep method in this thesis will be utilized to obtain series solutions of the initial value problems directly without reducing to first order equations. The coefficients of the developed method will be stored in the code in the form of backward difference formula. The codes were executed in UNIX operating system and the algorithms were written in C language. The numerical results showed that the performance of the developed method is acceptable in terms of maximum error and number of iterations when solving second order nonlinear boundary value problem
format	Thesis
qualification_level	Master's degree
author	Jafri, Mahanum Diana
author_facet	Jafri, Mahanum Diana
author_sort	Jafri, Mahanum Diana
title	Solving second order boundary value problem by shooting technique using backward difference formulae
title_short	Solving second order boundary value problem by shooting technique using backward difference formulae
title_full	Solving second order boundary value problem by shooting technique using backward difference formulae
title_fullStr	Solving second order boundary value problem by shooting technique using backward difference formulae
title_full_unstemmed	Solving second order boundary value problem by shooting technique using backward difference formulae
title_sort	solving second order boundary value problem by shooting technique using backward difference formulae
granting_institution	Universiti Putra Malaysia
granting_department	Institute for Mathematical Research
publishDate	2011
url	http://psasir.upm.edu.my/id/eprint/26514/1/IPM%202011%2020R.pdf
_version_	1747811545704824832

Solving second order boundary value problem by shooting technique using backward difference formulae

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