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Adam’s type block methods for solving neutral delay differential equation with constant and panthograph delay

The numerical solutions for Neutral Delay Differential Equation (NDDE) have been studied in this thesis. Two numerical methods which are known as an explicit multi- step block method and a hybrid multistep block method have been introduced. The multistep block methods will be implemented in s...

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Main Author: Ismail, Nur Inshirah Naqiah
Format: Thesis
Language:English
Published: 2019
Subjects:
Differential equations - Numerical solutions
Numerical analysis
Online Access:http://psasir.upm.edu.my/id/eprint/85750/1/IPM%202020%203%20-%20ir.pdf
http://psasir.upm.edu.my/id/eprint/85750/
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spelling my.upm.eprints.857502021-12-08T01:27:31Z http://psasir.upm.edu.my/id/eprint/85750/ Adam’s type block methods for solving neutral delay differential equation with constant and panthograph delay Ismail, Nur Inshirah Naqiah The numerical solutions for Neutral Delay Differential Equation (NDDE) have been studied in this thesis. Two numerical methods which are known as an explicit multi- step block method and a hybrid multistep block method have been introduced. The multistep block methods will be implemented in solving NDDE with constant and pantograph delay types using constant step size. Both methods have been derived by using Taylor series polynomial where the implementations of the methods are based on predictor-corrector formulas. In this research, the source codes for the numerical solutions were written in C language. In the developed algorithm, the delay terms have been approximated by using divided difference formulas depending on the ap- plicability of both methods in every iteration. Both constant and pantograph delay types have their own uniqueness in finding the solutions of the delay terms. The order, consistency and zero-stability for the block methods have been determined to ensure their applicability in solving both types of NDDE. The convergence and sta- bility analysis have also been analyzed. The stability polynomials for both multistep block methods have been obtained and their stability regions have been discussed. In conclusion, the numerical results obtained have proven that the proposed block methods give accurate results in terms of maximum and average error. The block methods have also produced less computational time in solving NDDE with con- stant and pantograph delay types. 2019-11 Thesis NonPeerReviewed text en http://psasir.upm.edu.my/id/eprint/85750/1/IPM%202020%203%20-%20ir.pdf Ismail, Nur Inshirah Naqiah (2019) Adam’s type block methods for solving neutral delay differential equation with constant and panthograph delay. Masters thesis, Universiti Putra Malaysia. Differential equations - Numerical solutions Numerical analysis
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
topic Differential equations - Numerical solutions
Numerical analysis
spellingShingle Differential equations - Numerical solutions
Numerical analysis
Ismail, Nur Inshirah Naqiah
Adam’s type block methods for solving neutral delay differential equation with constant and panthograph delay
description The numerical solutions for Neutral Delay Differential Equation (NDDE) have been studied in this thesis. Two numerical methods which are known as an explicit multi- step block method and a hybrid multistep block method have been introduced. The multistep block methods will be implemented in solving NDDE with constant and pantograph delay types using constant step size. Both methods have been derived by using Taylor series polynomial where the implementations of the methods are based on predictor-corrector formulas. In this research, the source codes for the numerical solutions were written in C language. In the developed algorithm, the delay terms have been approximated by using divided difference formulas depending on the ap- plicability of both methods in every iteration. Both constant and pantograph delay types have their own uniqueness in finding the solutions of the delay terms. The order, consistency and zero-stability for the block methods have been determined to ensure their applicability in solving both types of NDDE. The convergence and sta- bility analysis have also been analyzed. The stability polynomials for both multistep block methods have been obtained and their stability regions have been discussed. In conclusion, the numerical results obtained have proven that the proposed block methods give accurate results in terms of maximum and average error. The block methods have also produced less computational time in solving NDDE with con- stant and pantograph delay types.
format Thesis
author Ismail, Nur Inshirah Naqiah
author_facet Ismail, Nur Inshirah Naqiah
author_sort Ismail, Nur Inshirah Naqiah
title Adam’s type block methods for solving neutral delay differential equation with constant and panthograph delay
title_short Adam’s type block methods for solving neutral delay differential equation with constant and panthograph delay
title_full Adam’s type block methods for solving neutral delay differential equation with constant and panthograph delay
title_fullStr Adam’s type block methods for solving neutral delay differential equation with constant and panthograph delay
title_full_unstemmed Adam’s type block methods for solving neutral delay differential equation with constant and panthograph delay
title_sort adam’s type block methods for solving neutral delay differential equation with constant and panthograph delay
publishDate 2019
url http://psasir.upm.edu.my/id/eprint/85750/1/IPM%202020%203%20-%20ir.pdf
http://psasir.upm.edu.my/id/eprint/85750/
_version_ 1720438515597049856
score 13.211869

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