Solving higher order delay differential equations with boundary conditions using multistep block method

In this thesis, we derived two numerical methods called two point diagonally multistep block method order four and order five with the approach of predictorcorrector technique to solve higher order delay differential equations (DDEs) with boundary conditions. Shooting technique by using the Newto...

Full description

Saved in:

Bibliographic Details
Main Author:	Jaafar, Nur Tasnem
Format:	Thesis
Language:	English
Published:	2021
Subjects:	Differential equations Boundary value problems
Online Access:	http://psasir.upm.edu.my/id/eprint/98787/1/IPM%202021%2015%20%20-%20IR.pdf
Tags:	Add Tag No Tags, Be the first to tag this record!

id	my-upm-ir.98787
record_format	uketd_dc
spelling	my-upm-ir.987872022-09-20T01:41:30Z Solving higher order delay differential equations with boundary conditions using multistep block method 2021-04 Jaafar, Nur Tasnem In this thesis, we derived two numerical methods called two point diagonally multistep block method order four and order five with the approach of predictorcorrector technique to solve higher order delay differential equations (DDEs) with boundary conditions. Shooting technique by using the Newton’s like method is implemented to solve the boundary value problems (BVPs). This thesis begins with solving second order DDEs with constant, pantograph and time dependent delay type by using both methods. Then, those methods are extended to solve third order DDEs with constant and pantograph delay type. The approach used to solve constant delay type is by taking the previously calculated solutions at the delay terms while for pantograph and time dependent delay types, the approaches are by using the Lagrange interpolation to approximate the solutions at the delay terms. The derivatives present in the problems at the delay terms will be approximated by using the finite difference method. The analysis of both methods in terms of order, local truncation error and stability are also investigated. Two stability test equations are used to analyze the stability regions of the block methods. Several numerical problems are illustrated to solve by using C programming. The accuracy of the methods in terms of maximum and average errors along with the total function calls, total iteration steps, total guessing numbers for shooting technique are discussed and compared with the previous methods. In conclusion, the higher order DDEs with boundary conditions can be solved by using the proposed block methods based on the analysis of the methods and their numerical results. Differential equations Boundary value problems 2021-04 Thesis http://psasir.upm.edu.my/id/eprint/98787/ http://psasir.upm.edu.my/id/eprint/98787/1/IPM%202021%2015%20%20-%20IR.pdf text en public doctoral Universiti Putra Malaysia Differential equations Boundary value problems Abdul Majid, Zanariah
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English
advisor	Abdul Majid, Zanariah
topic	Differential equations Boundary value problems
spellingShingle	Differential equations Boundary value problems Jaafar, Nur Tasnem Solving higher order delay differential equations with boundary conditions using multistep block method
description	In this thesis, we derived two numerical methods called two point diagonally multistep block method order four and order five with the approach of predictorcorrector technique to solve higher order delay differential equations (DDEs) with boundary conditions. Shooting technique by using the Newton’s like method is implemented to solve the boundary value problems (BVPs). This thesis begins with solving second order DDEs with constant, pantograph and time dependent delay type by using both methods. Then, those methods are extended to solve third order DDEs with constant and pantograph delay type. The approach used to solve constant delay type is by taking the previously calculated solutions at the delay terms while for pantograph and time dependent delay types, the approaches are by using the Lagrange interpolation to approximate the solutions at the delay terms. The derivatives present in the problems at the delay terms will be approximated by using the finite difference method. The analysis of both methods in terms of order, local truncation error and stability are also investigated. Two stability test equations are used to analyze the stability regions of the block methods. Several numerical problems are illustrated to solve by using C programming. The accuracy of the methods in terms of maximum and average errors along with the total function calls, total iteration steps, total guessing numbers for shooting technique are discussed and compared with the previous methods. In conclusion, the higher order DDEs with boundary conditions can be solved by using the proposed block methods based on the analysis of the methods and their numerical results.
format	Thesis
qualification_level	Doctorate
author	Jaafar, Nur Tasnem
author_facet	Jaafar, Nur Tasnem
author_sort	Jaafar, Nur Tasnem
title	Solving higher order delay differential equations with boundary conditions using multistep block method
title_short	Solving higher order delay differential equations with boundary conditions using multistep block method
title_full	Solving higher order delay differential equations with boundary conditions using multistep block method
title_fullStr	Solving higher order delay differential equations with boundary conditions using multistep block method
title_full_unstemmed	Solving higher order delay differential equations with boundary conditions using multistep block method
title_sort	solving higher order delay differential equations with boundary conditions using multistep block method
granting_institution	Universiti Putra Malaysia
publishDate	2021
url	http://psasir.upm.edu.my/id/eprint/98787/1/IPM%202021%2015%20%20-%20IR.pdf
_version_	1747813891424911360

Solving higher order delay differential equations with boundary conditions using multistep block method

Similar Items