Numerical solution of special second order initial value problems by hybrid type methods

We derived in this thesis new highly dispersive and highly dissipative two-step explicit hybrid methods for solving oscillatory problems. Dispersion conditions up to order ten and dissipation conditions up to order eleven for five stage hybrid methods are presented. The derivation of the methods was...

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Main Author:	Dauda Yusuf Jikantoro
Format:	Thesis
Language:	English
Published:	2014
Subjects:	Mathematical analysis Differential equations Differential equations - Numerical solutions
Online Access:	http://psasir.upm.edu.my/id/eprint/55672/1/FS%202014%2035RR.pdf
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id	my-upm-ir.55672
record_format	uketd_dc
spelling	my-upm-ir.556722017-06-06T02:03:58Z Numerical solution of special second order initial value problems by hybrid type methods 2014-03 Dauda Yusuf Jikantoro, We derived in this thesis new highly dispersive and highly dissipative two-step explicit hybrid methods for solving oscillatory problems. Dispersion conditions up to order ten and dissipation conditions up to order eleven for five stage hybrid methods are presented. The derivation of the methods was largely based on maximization of order of dispersion and dissipation while minimizing the principal error norm. Stability of the methods was investigated and their intervals of stability presented. The methods, which can be applied using constant step size,were tested on model problems. Numerical results revealed the superiority of the methods over several existing methods in the literature. In order to achieve higher accuracy and efficiency, trigonometrically fitted hybrid methods based on existing zero-dissipative methods were derived. Their ability to approximate the solution of problems with large fitted frequency using large step size proved their accuracy and efficiency for solving highly oscillatory problems compared to phase-fitted methods and trigonometrically fitted methods which are based on dissipative hybrid methods. Finally, semi-implicit hybrid methods based on explicit hybrid methods were derived.Dispersion and dissipation conditions for the methods were presented. Stability analysis along side stability or periodicity intervals of the methods was presented.Results obtained from numerical experiment showed the accuracy and efficiency of the new methods compared to the existing methods. Mathematical analysis Differential equations Differential equations - Numerical solutions 2014-03 Thesis http://psasir.upm.edu.my/id/eprint/55672/ http://psasir.upm.edu.my/id/eprint/55672/1/FS%202014%2035RR.pdf application/pdf en public masters Universiti Putra Malaysia Mathematical analysis Differential equations Differential equations - Numerical solutions
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English
topic	Mathematical analysis Differential equations Differential equations - Numerical solutions
spellingShingle	Mathematical analysis Differential equations Differential equations - Numerical solutions Dauda Yusuf Jikantoro, Numerical solution of special second order initial value problems by hybrid type methods
description	We derived in this thesis new highly dispersive and highly dissipative two-step explicit hybrid methods for solving oscillatory problems. Dispersion conditions up to order ten and dissipation conditions up to order eleven for five stage hybrid methods are presented. The derivation of the methods was largely based on maximization of order of dispersion and dissipation while minimizing the principal error norm. Stability of the methods was investigated and their intervals of stability presented. The methods, which can be applied using constant step size,were tested on model problems. Numerical results revealed the superiority of the methods over several existing methods in the literature. In order to achieve higher accuracy and efficiency, trigonometrically fitted hybrid methods based on existing zero-dissipative methods were derived. Their ability to approximate the solution of problems with large fitted frequency using large step size proved their accuracy and efficiency for solving highly oscillatory problems compared to phase-fitted methods and trigonometrically fitted methods which are based on dissipative hybrid methods. Finally, semi-implicit hybrid methods based on explicit hybrid methods were derived.Dispersion and dissipation conditions for the methods were presented. Stability analysis along side stability or periodicity intervals of the methods was presented.Results obtained from numerical experiment showed the accuracy and efficiency of the new methods compared to the existing methods.
format	Thesis
qualification_level	Master's degree
author	Dauda Yusuf Jikantoro,
author_facet	Dauda Yusuf Jikantoro,
author_sort	Dauda Yusuf Jikantoro,
title	Numerical solution of special second order initial value problems by hybrid type methods
title_short	Numerical solution of special second order initial value problems by hybrid type methods
title_full	Numerical solution of special second order initial value problems by hybrid type methods
title_fullStr	Numerical solution of special second order initial value problems by hybrid type methods
title_full_unstemmed	Numerical solution of special second order initial value problems by hybrid type methods
title_sort	numerical solution of special second order initial value problems by hybrid type methods
granting_institution	Universiti Putra Malaysia
publishDate	2014
url	http://psasir.upm.edu.my/id/eprint/55672/1/FS%202014%2035RR.pdf
_version_	1747812108609781760

Numerical solution of special second order initial value problems by hybrid type methods

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