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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
Online Access:http://psasir.upm.edu.my/id/eprint/26514/1/IPM%202011%2020R.pdf
http://psasir.upm.edu.my/id/eprint/26514/
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spelling my.upm.eprints.265142014-11-28T08:02:17Z http://psasir.upm.edu.my/id/eprint/26514/ Solving second order boundary value problem by shooting technique using backward difference formulae 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 2011-11 Thesis NonPeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/26514/1/IPM%202011%2020R.pdf Jafri, Mahanum Diana (2011) Solving second order boundary value problem by shooting technique using backward difference formulae. Masters thesis, Universiti Putra Malaysia.
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
language English
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
author Jafri, Mahanum Diana
spellingShingle Jafri, Mahanum Diana
Solving second order boundary value problem by shooting technique using backward difference formulae
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
publishDate 2011
url http://psasir.upm.edu.my/id/eprint/26514/1/IPM%202011%2020R.pdf
http://psasir.upm.edu.my/id/eprint/26514/
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score 13.211869

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