Direct one-step block methods for solving special second order delay differential equations

This thesis describes the implementation of one-step block methods of Runge-Kutta type for solving second order Delay Differential Equations (DDEs). The one-step block method will solve the second order DDEs directly without reducing to first order equations. The solution will be approximated simult...

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Main Author: Rasdi, Nadzirah
Format: Thesis
Language:English
Published: 2013
Online Access:http://psasir.upm.edu.my/id/eprint/39139/1/FS%202013%2038%20IR.pdf
http://psasir.upm.edu.my/id/eprint/39139/
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Institution: Universiti Putra Malaysia
Language: English
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spelling my.upm.eprints.391392016-04-11T09:24:17Z http://psasir.upm.edu.my/id/eprint/39139/ Direct one-step block methods for solving special second order delay differential equations Rasdi, Nadzirah This thesis describes the implementation of one-step block methods of Runge-Kutta type for solving second order Delay Differential Equations (DDEs). The one-step block method will solve the second order DDEs directly without reducing to first order equations. The solution will be approximated simultaneously at more than one point based on equidistant block method and each of these values is calculated independently of each other. In this research, the block methods are implemented based on the predictor-corrector scheme using constant step size technique. The derivation of two point, three point, extended two point and extended three point implicit block methods were also described. Those methods were derived using Lagrange interpolation polynomial. The stability polynomials for the methods are obtained and their regions of absolute stability are discussed. Subsequently, the one-step block methods were then adapted to solve delay differential equations. The basic idea is to apply the same integration method and use interpolation polynomial to approximate the solution in the previous value. The efficiency of the proposed block method is supported by some numerical results. The results showed that the block methods proposed in this thesis are suitable to solve second order DDEs. 2013-05 Thesis NonPeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/39139/1/FS%202013%2038%20IR.pdf Rasdi, Nadzirah (2013) Direct one-step block methods for solving special second order delay differential equations. 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 This thesis describes the implementation of one-step block methods of Runge-Kutta type for solving second order Delay Differential Equations (DDEs). The one-step block method will solve the second order DDEs directly without reducing to first order equations. The solution will be approximated simultaneously at more than one point based on equidistant block method and each of these values is calculated independently of each other. In this research, the block methods are implemented based on the predictor-corrector scheme using constant step size technique. The derivation of two point, three point, extended two point and extended three point implicit block methods were also described. Those methods were derived using Lagrange interpolation polynomial. The stability polynomials for the methods are obtained and their regions of absolute stability are discussed. Subsequently, the one-step block methods were then adapted to solve delay differential equations. The basic idea is to apply the same integration method and use interpolation polynomial to approximate the solution in the previous value. The efficiency of the proposed block method is supported by some numerical results. The results showed that the block methods proposed in this thesis are suitable to solve second order DDEs.
format Thesis
author Rasdi, Nadzirah
spellingShingle Rasdi, Nadzirah
Direct one-step block methods for solving special second order delay differential equations
author_facet Rasdi, Nadzirah
author_sort Rasdi, Nadzirah
title Direct one-step block methods for solving special second order delay differential equations
title_short Direct one-step block methods for solving special second order delay differential equations
title_full Direct one-step block methods for solving special second order delay differential equations
title_fullStr Direct one-step block methods for solving special second order delay differential equations
title_full_unstemmed Direct one-step block methods for solving special second order delay differential equations
title_sort direct one-step block methods for solving special second order delay differential equations
publishDate 2013
url http://psasir.upm.edu.my/id/eprint/39139/1/FS%202013%2038%20IR.pdf
http://psasir.upm.edu.my/id/eprint/39139/
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