Explicit hybrid methods for solving special second order ordinary differential equations

The focus of this thesis is to derive new two-step explicit hybrid methods for the numerical solution of system of special second order ordinary differential equations of the form y"=f ( x, y) . Explicit hybrid methods of order seven have been developed by employing strategies of selecting fre...

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Main Author:	Samat, Faieza
Format:	Thesis
Language:	English
Published:	2012
Subjects:	Differential equations Hybrid system
Online Access:	http://psasir.upm.edu.my/id/eprint/33135/1/FS%202012%2060R.pdf
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id	my-upm-ir.33135
record_format	uketd_dc
spelling	my-upm-ir.331352015-03-04T07:15:38Z Explicit hybrid methods for solving special second order ordinary differential equations 2012-06 Samat, Faieza The focus of this thesis is to derive new two-step explicit hybrid methods for the numerical solution of system of special second order ordinary differential equations of the form y"=f ( x, y) . Explicit hybrid methods of order seven have been developed by employing strategies of selecting free parameters. Dissipation relations are imposed to obtain a method with highest possible order of dissipation. Phase-lag and stability analysis are presented. Numerical results show that the methods give better accuracy compared with the existing methods. For variable step-size codes,embedded pairs of explicit hybrid methods are introduced. The phase-lag and stability interval of the methods are given and the procedure of controlling the stepsize change is described. To improve the accuracy of hybrid methods, the construction of exponentially fitted explicit hybrid methods is investigated. The derivations of the methods with two stages and four stages are described in detail. The method with two stages is derived for constant step-size code whereas the method with four stages is derived for variable step-size code. Their stability regions and the numerical results are given. Finally, the construction of a block explicit hybrid method implemented on a parallel computer is discussed. This method calculates two consecutive points using two independent formulas. The stability analysis of the formula which computes the second point is presented. The parallel implementation of the method is evaluated in terms of accuracy and speedup. From the results, it is observed that the speedup is greater than 1.5 which indicates that the parallel code is faster than the sequential one. On the whole, this study reveals that the new methods are capable and efficient for solving special second order ordinary differential equations. Differential equations Hybrid system 2012-06 Thesis http://psasir.upm.edu.my/id/eprint/33135/ http://psasir.upm.edu.my/id/eprint/33135/1/FS%202012%2060R.pdf application/pdf en public phd doctoral Universiti Putra Malaysia Differential equations Hybrid system
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English
topic	Differential equations Hybrid system
spellingShingle	Differential equations Hybrid system Samat, Faieza Explicit hybrid methods for solving special second order ordinary differential equations
description	The focus of this thesis is to derive new two-step explicit hybrid methods for the numerical solution of system of special second order ordinary differential equations of the form y"=f ( x, y) . Explicit hybrid methods of order seven have been developed by employing strategies of selecting free parameters. Dissipation relations are imposed to obtain a method with highest possible order of dissipation. Phase-lag and stability analysis are presented. Numerical results show that the methods give better accuracy compared with the existing methods. For variable step-size codes,embedded pairs of explicit hybrid methods are introduced. The phase-lag and stability interval of the methods are given and the procedure of controlling the stepsize change is described. To improve the accuracy of hybrid methods, the construction of exponentially fitted explicit hybrid methods is investigated. The derivations of the methods with two stages and four stages are described in detail. The method with two stages is derived for constant step-size code whereas the method with four stages is derived for variable step-size code. Their stability regions and the numerical results are given. Finally, the construction of a block explicit hybrid method implemented on a parallel computer is discussed. This method calculates two consecutive points using two independent formulas. The stability analysis of the formula which computes the second point is presented. The parallel implementation of the method is evaluated in terms of accuracy and speedup. From the results, it is observed that the speedup is greater than 1.5 which indicates that the parallel code is faster than the sequential one. On the whole, this study reveals that the new methods are capable and efficient for solving special second order ordinary differential equations.
format	Thesis
qualification_name	Doctor of Philosophy (PhD.)
qualification_level	Doctorate
author	Samat, Faieza
author_facet	Samat, Faieza
author_sort	Samat, Faieza
title	Explicit hybrid methods for solving special second order ordinary differential equations
title_short	Explicit hybrid methods for solving special second order ordinary differential equations
title_full	Explicit hybrid methods for solving special second order ordinary differential equations
title_fullStr	Explicit hybrid methods for solving special second order ordinary differential equations
title_full_unstemmed	Explicit hybrid methods for solving special second order ordinary differential equations
title_sort	explicit hybrid methods for solving special second order ordinary differential equations
granting_institution	Universiti Putra Malaysia
publishDate	2012
url	http://psasir.upm.edu.my/id/eprint/33135/1/FS%202012%2060R.pdf
_version_	1747811687203864576

Explicit hybrid methods for solving special second order ordinary differential equations

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