New rational and pseudo type runge kutta methods for first order initial value problems

Unconventional methods for the numerical solution of first order initial value problems (IVPs) are well established in the past decades. There are two major reasons that motivate the developments of unconventional methods: firstly, unconventional methods are developed to solve certain types of IVPs,...

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Main Author:	Teh, Yuan Ying
Format:	Thesis
Language:	English
Published:	2010
Subjects:	QA Mathematics
Online Access:	http://eprints.utm.my/id/eprint/18777/16/TehYuanYingPFSA2010.pdf
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spelling	my-utm-ep.187772017-09-13T07:17:36Z New rational and pseudo type runge kutta methods for first order initial value problems 2010 Teh, Yuan Ying QA Mathematics Unconventional methods for the numerical solution of first order initial value problems (IVPs) are well established in the past decades. There are two major reasons that motivate the developments of unconventional methods: firstly, unconventional methods are developed to solve certain types of IVPs, such as IVPs with oscillatory solutions or IVPs whose solutions possess singularities, where in most of the time, conventional methods will perform poorly; and secondly, unconventional methods might possess some outstanding features that could never be achieved by conventional methods. These features include achieving high order of numerical accuracy with less computational cost, stronger stability properties and so on. In this thesis, some studies are made of the unconventional methods based on rational functions and mean expressions. The study has led to the discovery of some new exponential-rational methods and rational multistep methods which can be used effectively for numerical solution of first order IVPs. The study continues with the discoveries of some new pseudo Runge-Kutta methods based on harmonic and arithmetic means; and a multistep method based on centroidal mean, which are found to be effective for the numerical solution of first order IVPs. This thesis also includes the study of implicit Runge-Kutta (IRK) methods, which led to the developments of three new classes of IRK methods based on Kronrod-type quadrature formulae. Each new method developed in this thesis is furnished with local truncation error and absolute stability analysis. In addition, each new method is tested on some test problems and also compared with other conventional or classical methods in the same order. 2010 Thesis http://eprints.utm.my/id/eprint/18777/ http://eprints.utm.my/id/eprint/18777/16/TehYuanYingPFSA2010.pdf application/pdf en public phd doctoral Universiti Teknologi Malaysia, Faculty of Science Faculty of Science
institution	Universiti Teknologi Malaysia
collection	UTM Institutional Repository
language	English
topic	QA Mathematics
spellingShingle	QA Mathematics Teh, Yuan Ying New rational and pseudo type runge kutta methods for first order initial value problems
description	Unconventional methods for the numerical solution of first order initial value problems (IVPs) are well established in the past decades. There are two major reasons that motivate the developments of unconventional methods: firstly, unconventional methods are developed to solve certain types of IVPs, such as IVPs with oscillatory solutions or IVPs whose solutions possess singularities, where in most of the time, conventional methods will perform poorly; and secondly, unconventional methods might possess some outstanding features that could never be achieved by conventional methods. These features include achieving high order of numerical accuracy with less computational cost, stronger stability properties and so on. In this thesis, some studies are made of the unconventional methods based on rational functions and mean expressions. The study has led to the discovery of some new exponential-rational methods and rational multistep methods which can be used effectively for numerical solution of first order IVPs. The study continues with the discoveries of some new pseudo Runge-Kutta methods based on harmonic and arithmetic means; and a multistep method based on centroidal mean, which are found to be effective for the numerical solution of first order IVPs. This thesis also includes the study of implicit Runge-Kutta (IRK) methods, which led to the developments of three new classes of IRK methods based on Kronrod-type quadrature formulae. Each new method developed in this thesis is furnished with local truncation error and absolute stability analysis. In addition, each new method is tested on some test problems and also compared with other conventional or classical methods in the same order.
format	Thesis
qualification_name	Doctor of Philosophy (PhD.)
qualification_level	Doctorate
author	Teh, Yuan Ying
author_facet	Teh, Yuan Ying
author_sort	Teh, Yuan Ying
title	New rational and pseudo type runge kutta methods for first order initial value problems
title_short	New rational and pseudo type runge kutta methods for first order initial value problems
title_full	New rational and pseudo type runge kutta methods for first order initial value problems
title_fullStr	New rational and pseudo type runge kutta methods for first order initial value problems
title_full_unstemmed	New rational and pseudo type runge kutta methods for first order initial value problems
title_sort	new rational and pseudo type runge kutta methods for first order initial value problems
granting_institution	Universiti Teknologi Malaysia, Faculty of Science
granting_department	Faculty of Science
publishDate	2010
url	http://eprints.utm.my/id/eprint/18777/16/TehYuanYingPFSA2010.pdf
_version_	1747815356276146176

New rational and pseudo type runge kutta methods for first order initial value problems

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