Solving third-order boundary value problem by direct methods

Solving third-order boundary value problem by direct methods

In this research, the direct method of multistep method is developed for the numerical solution of nonlinear boundary value problems (BVPs) of Type 1 and Type 2 directly. Most of the existing research involving BVPs will reduce the problem to a system of first order Ordinary Differential Equations...

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Main Author: Ahmad Zulkifli, Ahmad Shah Abdullah
Format: Thesis
Language:English
Published: 2014
Subjects:
Differential equations
Boundary value problems - Numerical solutions
Online Access:http://psasir.upm.edu.my/id/eprint/38487/1/IPM%202014%202%20IR.pdf
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spelling my-upm-ir.384872017-01-13T08:16:55Z Solving third-order boundary value problem by direct methods 2014-02 Ahmad Zulkifli, Ahmad Shah Abdullah In this research, the direct method of multistep method is developed for the numerical solution of nonlinear boundary value problems (BVPs) of Type 1 and Type 2 directly. Most of the existing research involving BVPs will reduce the problem to a system of first order Ordinary Differential Equations (ODEs). However, the proposed method will solve the third-order BVPs directly without reducing to first-order ODEs with constant step size using the shooting technique. On- point and two-point direct block method of Adam Moulton have been derived. These methods consists the predictor and corrector method where the predictor is one order less than the corrector. In the numerical results, one-point direct methods have advantages in accuracy and for two-point direct block methods have advantages in timing calculation. The results clearly show that the proposed method is suitable for solving third-order nonlinear BVPs. Differential equations Boundary value problems - Numerical solutions 2014-02 Thesis http://psasir.upm.edu.my/id/eprint/38487/ http://psasir.upm.edu.my/id/eprint/38487/1/IPM%202014%202%20IR.pdf application/pdf en public masters Universiti Putra Malaysia Differential equations Boundary value problems - Numerical solutions
institution Universiti Putra Malaysia
collection PSAS Institutional Repository
language English
topic Differential equations
Boundary value problems - Numerical solutions
spellingShingle Differential equations
Boundary value problems - Numerical solutions

Ahmad Zulkifli, Ahmad Shah Abdullah
Solving third-order boundary value problem by direct methods
description In this research, the direct method of multistep method is developed for the numerical solution of nonlinear boundary value problems (BVPs) of Type 1 and Type 2 directly. Most of the existing research involving BVPs will reduce the problem to a system of first order Ordinary Differential Equations (ODEs). However, the proposed method will solve the third-order BVPs directly without reducing to first-order ODEs with constant step size using the shooting technique. On- point and two-point direct block method of Adam Moulton have been derived. These methods consists the predictor and corrector method where the predictor is one order less than the corrector. In the numerical results, one-point direct methods have advantages in accuracy and for two-point direct block methods have advantages in timing calculation. The results clearly show that the proposed method is suitable for solving third-order nonlinear BVPs.
format Thesis
qualification_level Master's degree
author Ahmad Zulkifli, Ahmad Shah Abdullah
author_facet Ahmad Zulkifli, Ahmad Shah Abdullah
author_sort Ahmad Zulkifli, Ahmad Shah Abdullah
title Solving third-order boundary value problem by direct methods
title_short Solving third-order boundary value problem by direct methods
title_full Solving third-order boundary value problem by direct methods
title_fullStr Solving third-order boundary value problem by direct methods
title_full_unstemmed Solving third-order boundary value problem by direct methods
title_sort solving third-order boundary value problem by direct methods
granting_institution Universiti Putra Malaysia
publishDate 2014
url http://psasir.upm.edu.my/id/eprint/38487/1/IPM%202014%202%20IR.pdf
_version_ 1747811720649244672

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