Backward differentiation formulae with variable stepsize variable order for solving stiff delay differential equations / Nora Baizura Mohd Isa

This thesis describes the development of predictor-corrector variable stepsize variable order based on backward differentiation formulae (BVSVO) method and direct predictor-corrector variable stepsize variable order based on backward differentiation formulae (DBVSVO) method for solving first order...

Full description

Bibliographic Details
Main Author:	Mohd Isa, Nora Baizura
Format:	Thesis
Language:	English
Published:	2015
Subjects:	QA Mathematics Mathematical statistics. Probabilities
Online Access:	http://ir.uitm.edu.my/id/eprint/15139/ http://ir.uitm.edu.my/id/eprint/15139/1/TM_NORA%20BAIZURA%20MOHD%20ISA%20CS%2015_5.pdf

id	uitm-15139
recordtype	eprints
spelling	uitm-151392016-11-10T02:26:26Z http://ir.uitm.edu.my/id/eprint/15139/ Backward differentiation formulae with variable stepsize variable order for solving stiff delay differential equations / Nora Baizura Mohd Isa Mohd Isa, Nora Baizura QA Mathematics Mathematical statistics. Probabilities This thesis describes the development of predictor-corrector variable stepsize variable order based on backward differentiation formulae (BVSVO) method and direct predictor-corrector variable stepsize variable order based on backward differentiation formulae (DBVSVO) method for solving first order and special second order stiff delay differential equations respectively. The predictor and corrector formulae are represented in divided difference form. The developed methods are implemented using variable stepsize variable order technique. In varying the stepsize, the coefficients of the methods need to be recomputed at every step which will create extra computational cost. Thus, in order to reduce the computational cost, the coefficients of the methods are computed by a simple recurrence relation. In solving first order stiff delay differential equations using the BVSVO method, the numerical results are compared with non-stiff method, single-step method and multistep method.From the numerical results, the BVSVO method has shown the efficiency and reliability for solving first order stiff delay differential equations in terms of total number of steps, maximum error and average error. The DBVSVO method is used to solve special second order stiff delay differential equations directly without reducing to first order equations. We present some test examples to check an accuracy and efficiency of the DBVSVO method. For comparison purposes, the same set of test examples is reduced to a system of first order equations and solved using the BVSVO method. The numerical results for solving special second order stiff delay differential equations using the DBVSVO method is better compared with the BVSVO method in term of total number of function evaluations 2015 Thesis NonPeerReviewed text en http://ir.uitm.edu.my/id/eprint/15139/1/TM_NORA%20BAIZURA%20MOHD%20ISA%20CS%2015_5.pdf Mohd Isa, Nora Baizura (2015) Backward differentiation formulae with variable stepsize variable order for solving stiff delay differential equations / Nora Baizura Mohd Isa. Masters thesis, Universiti Teknologi MARA.
repository_type	Digital Repository
institution_category	Local University
institution	Universiti Teknologi MARA
building	UiTM Institutional Repository
collection	Online Access
language	English
topic	QA Mathematics Mathematical statistics. Probabilities
spellingShingle	QA Mathematics Mathematical statistics. Probabilities Mohd Isa, Nora Baizura Backward differentiation formulae with variable stepsize variable order for solving stiff delay differential equations / Nora Baizura Mohd Isa
description	This thesis describes the development of predictor-corrector variable stepsize variable order based on backward differentiation formulae (BVSVO) method and direct predictor-corrector variable stepsize variable order based on backward differentiation formulae (DBVSVO) method for solving first order and special second order stiff delay differential equations respectively. The predictor and corrector formulae are represented in divided difference form. The developed methods are implemented using variable stepsize variable order technique. In varying the stepsize, the coefficients of the methods need to be recomputed at every step which will create extra computational cost. Thus, in order to reduce the computational cost, the coefficients of the methods are computed by a simple recurrence relation. In solving first order stiff delay differential equations using the BVSVO method, the numerical results are compared with non-stiff method, single-step method and multistep method.From the numerical results, the BVSVO method has shown the efficiency and reliability for solving first order stiff delay differential equations in terms of total number of steps, maximum error and average error. The DBVSVO method is used to solve special second order stiff delay differential equations directly without reducing to first order equations. We present some test examples to check an accuracy and efficiency of the DBVSVO method. For comparison purposes, the same set of test examples is reduced to a system of first order equations and solved using the BVSVO method. The numerical results for solving special second order stiff delay differential equations using the DBVSVO method is better compared with the BVSVO method in term of total number of function evaluations
format	Thesis
author	Mohd Isa, Nora Baizura
author_facet	Mohd Isa, Nora Baizura
author_sort	Mohd Isa, Nora Baizura
title	Backward differentiation formulae with variable stepsize variable order for solving stiff delay differential equations / Nora Baizura Mohd Isa
title_short	Backward differentiation formulae with variable stepsize variable order for solving stiff delay differential equations / Nora Baizura Mohd Isa
title_full	Backward differentiation formulae with variable stepsize variable order for solving stiff delay differential equations / Nora Baizura Mohd Isa
title_fullStr	Backward differentiation formulae with variable stepsize variable order for solving stiff delay differential equations / Nora Baizura Mohd Isa
title_full_unstemmed	Backward differentiation formulae with variable stepsize variable order for solving stiff delay differential equations / Nora Baizura Mohd Isa
title_sort	backward differentiation formulae with variable stepsize variable order for solving stiff delay differential equations / nora baizura mohd isa
publishDate	2015
url	http://ir.uitm.edu.my/id/eprint/15139/ http://ir.uitm.edu.my/id/eprint/15139/1/TM_NORA%20BAIZURA%20MOHD%20ISA%20CS%2015_5.pdf
first_indexed	2023-09-18T22:53:12Z
last_indexed	2023-09-18T22:53:12Z
_version_	1777417681177149440

Backward differentiation formulae with variable stepsize variable order for solving stiff delay differential equations / Nora Baizura Mohd Isa

Similar Items