Multistep block methods for solving higher order delay differential equations

Delay differential equations (DDEs) play an important role in the investigated system which depends on the position of the system in the past and current time. The analytical solution of DDEs is hard to be found. Numerical methods provide an alternative way of constructing solutions to the proble...

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Main Author:	Hoo, Yann Seong
Format:	Thesis
Language:	English
Published:	2016
Subjects:	Delay differential equations - Numerical solutions
Online Access:	http://psasir.upm.edu.my/id/eprint/69261/1/FS%202016%2061%20-%20IR.pdf
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spelling	my-upm-ir.692612019-06-27T01:37:15Z Multistep block methods for solving higher order delay differential equations 2016-05 Hoo, Yann Seong Delay differential equations (DDEs) play an important role in the investigated system which depends on the position of the system in the past and current time. The analytical solution of DDEs is hard to be found. Numerical methods provide an alternative way of constructing solutions to the problems. This thesis describes the development of numerical algorithms for solving higher order DDEs. One-point and two-point multistep block method based on the Adam-Bashforth- Moulton methods for solving higher ordinary differential equation are adapted to solve the higher order DDEs. The proposed methods are based on constant step size and variable step size approach. Two types of DDEs are considered, namely retarded and neutral DDEs. Only the DDEs with constant delays and pantograph type are considered in this thesis. The delay term in DDEs with constant delays is approximated using Hermite interpolation. Linear and Hermite interpolators are used to approximate the delay terms in DDEs of pantograph type. The derivatives of the delay terms are approximated by using difference formula. The thesis discusses the stability of the method when applied to DDEs with constant delays and pantograph type. The region of the stability is presented. Several problems are considered for illustrative purposes and the numerical approximations of their solutions are obtained using C-language. Numerical results of the proposed methods are compared with the existing numerical methods. Comparison among the methods indicated that the proposed methods achieve the desired accuracy. Block method are efficient when compare with the non-block method as the total steps taken can be reduced. Delay differential equations - Numerical solutions Differential equations, Linear - Numerical solutions 2016-05 Thesis http://psasir.upm.edu.my/id/eprint/69261/ http://psasir.upm.edu.my/id/eprint/69261/1/FS%202016%2061%20-%20IR.pdf text en public doctoral Universiti Putra Malaysia Delay differential equations - Numerical solutions Differential equations, Linear - Numerical solutions
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English
topic	Delay differential equations - Numerical solutions Delay differential equations - Numerical solutions
spellingShingle	Delay differential equations - Numerical solutions Delay differential equations - Numerical solutions Hoo, Yann Seong Multistep block methods for solving higher order delay differential equations
description	Delay differential equations (DDEs) play an important role in the investigated system which depends on the position of the system in the past and current time. The analytical solution of DDEs is hard to be found. Numerical methods provide an alternative way of constructing solutions to the problems. This thesis describes the development of numerical algorithms for solving higher order DDEs. One-point and two-point multistep block method based on the Adam-Bashforth- Moulton methods for solving higher ordinary differential equation are adapted to solve the higher order DDEs. The proposed methods are based on constant step size and variable step size approach. Two types of DDEs are considered, namely retarded and neutral DDEs. Only the DDEs with constant delays and pantograph type are considered in this thesis. The delay term in DDEs with constant delays is approximated using Hermite interpolation. Linear and Hermite interpolators are used to approximate the delay terms in DDEs of pantograph type. The derivatives of the delay terms are approximated by using difference formula. The thesis discusses the stability of the method when applied to DDEs with constant delays and pantograph type. The region of the stability is presented. Several problems are considered for illustrative purposes and the numerical approximations of their solutions are obtained using C-language. Numerical results of the proposed methods are compared with the existing numerical methods. Comparison among the methods indicated that the proposed methods achieve the desired accuracy. Block method are efficient when compare with the non-block method as the total steps taken can be reduced.
format	Thesis
qualification_level	Doctorate
author	Hoo, Yann Seong
author_facet	Hoo, Yann Seong
author_sort	Hoo, Yann Seong
title	Multistep block methods for solving higher order delay differential equations
title_short	Multistep block methods for solving higher order delay differential equations
title_full	Multistep block methods for solving higher order delay differential equations
title_fullStr	Multistep block methods for solving higher order delay differential equations
title_full_unstemmed	Multistep block methods for solving higher order delay differential equations
title_sort	multistep block methods for solving higher order delay differential equations
granting_institution	Universiti Putra Malaysia
publishDate	2016
url	http://psasir.upm.edu.my/id/eprint/69261/1/FS%202016%2061%20-%20IR.pdf
_version_	1747812676151541760

Multistep block methods for solving higher order delay differential equations

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