Diagonally implicit block backward differentiation formula with off step points for solving stiff ordinary differential equations

This research demonstrates an alternative method for solving stiff ordinary differential equations (ODEs) using a diagonally implicit block backward differentiation formula with off-step points (DOBBDF). The off-step points are the optimal points between two equidistant grid points that help prov...

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Main Author:	Abd Rasid, Norshakila
Format:	Thesis
Language:	English
Published:	2021
Subjects:	Differential equations - Numerical solutions Stiff computation (Differential equations)
Online Access:	http://psasir.upm.edu.my/id/eprint/92775/1/FS%202021%2038%20-%20IR.pdf
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id	my-upm-ir.92775
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spelling	my-upm-ir.927752022-05-10T04:22:05Z Diagonally implicit block backward differentiation formula with off step points for solving stiff ordinary differential equations 2021-05 Abd Rasid, Norshakila This research demonstrates an alternative method for solving stiff ordinary differential equations (ODEs) using a diagonally implicit block backward differentiation formula with off-step points (DOBBDF). The off-step points are the optimal points between two equidistant grid points that help provided stable and high-accuracy solutions. The diagonally implicit form optimized the computational cost since fewer differential coefficients caused reducing the execution times. The thesis is divided into two significant parts. The first part showed the derivation and implementation of the two-point DOBBDF using constant and variable step-size strategies for solving the first-order stiff ODEs. The methods satisfied the convergence properties and A-stable conditions and yielded the region which contains the whole negative real axis in the complex plane. Numerical results revealed that the derived method excels than the other same kind methods. The second part described the formulation of DOBBDF for solving second-order ODEs directly. The direct method is the best feature to replace the previously expensive approach. The costly technique involved reducing the higher-order ODEs to first-order ODEs and solve using the first-order method. The new direct methods emphasized approximation at two solution points and two off-step points simultaneously in a block using constant and variable step-size strategies. The methods satisfied the properties of consistency and zero-stable, guaranteed convergent method for directly solving second-order Initial value problems of ODEs. Last, the DOBBDF is validated with several application models, including cancer, gene regulations, Prothero-Robinson system, and oscillation problems. In conclusion, DOBBDF is a significant alternative solver for the stiff ODEs model in science and engineering. Differential equations - Numerical solutions Stiff computation (Differential equations) 2021-05 Thesis http://psasir.upm.edu.my/id/eprint/92775/ http://psasir.upm.edu.my/id/eprint/92775/1/FS%202021%2038%20-%20IR.pdf text en public doctoral Universiti Putra Malaysia Differential equations - Numerical solutions Stiff computation (Differential equations) Ibrahim, Zarina Bibi
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English
advisor	Ibrahim, Zarina Bibi
topic	Differential equations - Numerical solutions Stiff computation (Differential equations)
spellingShingle	Differential equations - Numerical solutions Stiff computation (Differential equations) Abd Rasid, Norshakila Diagonally implicit block backward differentiation formula with off step points for solving stiff ordinary differential equations
description	This research demonstrates an alternative method for solving stiff ordinary differential equations (ODEs) using a diagonally implicit block backward differentiation formula with off-step points (DOBBDF). The off-step points are the optimal points between two equidistant grid points that help provided stable and high-accuracy solutions. The diagonally implicit form optimized the computational cost since fewer differential coefficients caused reducing the execution times. The thesis is divided into two significant parts. The first part showed the derivation and implementation of the two-point DOBBDF using constant and variable step-size strategies for solving the first-order stiff ODEs. The methods satisfied the convergence properties and A-stable conditions and yielded the region which contains the whole negative real axis in the complex plane. Numerical results revealed that the derived method excels than the other same kind methods. The second part described the formulation of DOBBDF for solving second-order ODEs directly. The direct method is the best feature to replace the previously expensive approach. The costly technique involved reducing the higher-order ODEs to first-order ODEs and solve using the first-order method. The new direct methods emphasized approximation at two solution points and two off-step points simultaneously in a block using constant and variable step-size strategies. The methods satisfied the properties of consistency and zero-stable, guaranteed convergent method for directly solving second-order Initial value problems of ODEs. Last, the DOBBDF is validated with several application models, including cancer, gene regulations, Prothero-Robinson system, and oscillation problems. In conclusion, DOBBDF is a significant alternative solver for the stiff ODEs model in science and engineering.
format	Thesis
qualification_level	Doctorate
author	Abd Rasid, Norshakila
author_facet	Abd Rasid, Norshakila
author_sort	Abd Rasid, Norshakila
title	Diagonally implicit block backward differentiation formula with off step points for solving stiff ordinary differential equations
title_short	Diagonally implicit block backward differentiation formula with off step points for solving stiff ordinary differential equations
title_full	Diagonally implicit block backward differentiation formula with off step points for solving stiff ordinary differential equations
title_fullStr	Diagonally implicit block backward differentiation formula with off step points for solving stiff ordinary differential equations
title_full_unstemmed	Diagonally implicit block backward differentiation formula with off step points for solving stiff ordinary differential equations
title_sort	diagonally implicit block backward differentiation formula with off step points for solving stiff ordinary differential equations
granting_institution	Universiti Putra Malaysia
publishDate	2021
url	http://psasir.upm.edu.my/id/eprint/92775/1/FS%202021%2038%20-%20IR.pdf
_version_	1747813763845718016

Diagonally implicit block backward differentiation formula with off step points for solving stiff ordinary differential equations

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