Numerical solutions of stiff ordinary differential equations and differential algebraic equations using one-step implicit hybrid methods

The numerical solutions of stiff ordinary differential equations and differential algebraic equations have been studied in this thesis. New one-step implicit hybrid methods are developed to solve stiff ordinary differential equations (ODEs) and semiexplicit index-1 differential algebraic equations...

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Main Author:	Khoo, Kai Wen
Format:	Thesis
Language:	English
Published:	2015
Subjects:	Differential equations - Numerical solutions Algebraic fields Stiff computation (Differential equations)
Online Access:	http://psasir.upm.edu.my/id/eprint/58929/1/IPM%202015%2014IR.pdf
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id	my-upm-ir.58929
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spelling	my-upm-ir.589292018-05-08T08:19:09Z Numerical solutions of stiff ordinary differential equations and differential algebraic equations using one-step implicit hybrid methods 2015-12 Khoo, Kai Wen The numerical solutions of stiff ordinary differential equations and differential algebraic equations have been studied in this thesis. New one-step implicit hybrid methods are developed to solve stiff ordinary differential equations (ODEs) and semiexplicit index-1 differential algebraic equations (DAEs). These methods are formulated by using Lagrange interpolating polynomial. The developed one-step methods will solve ODEs and DAEs with the introduction of off-step points by constant step size. The source codes were written in C language. Stiff equations in Mathematics indicate that for a certain numerical method to solve differential equations that may give unstable results unless the step size taken is extremely small. Newton’s iteration is implemented together with the developed method to solve stiff equations. The numerical results showed that the performance of the methods outperformed compared to existing method in terms of maximum error and average error. Further, this study is extended by using the developed method to solve DAEs. Semiexplicit index-1 DAEs is the system of ordinary differential equations with algebraic constrains. Newton’s iteration is implemented with the developed methods to solve DAEs. The numerical results showed the performance of the developed methods is more efficient then existing methods in terms of maximum error and average error. In conclusion, the proposed one-step implicit hybrid methods are suitable for solving stiff ordinary differential equations and semi-explicit index-1 differential algebraic equations. Differential equations - Numerical solutions Algebraic fields Stiff computation (Differential equations) 2015-12 Thesis http://psasir.upm.edu.my/id/eprint/58929/ http://psasir.upm.edu.my/id/eprint/58929/1/IPM%202015%2014IR.pdf application/pdf en public masters Universiti Putra Malaysia Differential equations - Numerical solutions Algebraic fields Stiff computation (Differential equations)
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English
topic	Differential equations - Numerical solutions Algebraic fields Stiff computation (Differential equations)
spellingShingle	Differential equations - Numerical solutions Algebraic fields Stiff computation (Differential equations) Khoo, Kai Wen Numerical solutions of stiff ordinary differential equations and differential algebraic equations using one-step implicit hybrid methods
description	The numerical solutions of stiff ordinary differential equations and differential algebraic equations have been studied in this thesis. New one-step implicit hybrid methods are developed to solve stiff ordinary differential equations (ODEs) and semiexplicit index-1 differential algebraic equations (DAEs). These methods are formulated by using Lagrange interpolating polynomial. The developed one-step methods will solve ODEs and DAEs with the introduction of off-step points by constant step size. The source codes were written in C language. Stiff equations in Mathematics indicate that for a certain numerical method to solve differential equations that may give unstable results unless the step size taken is extremely small. Newton’s iteration is implemented together with the developed method to solve stiff equations. The numerical results showed that the performance of the methods outperformed compared to existing method in terms of maximum error and average error. Further, this study is extended by using the developed method to solve DAEs. Semiexplicit index-1 DAEs is the system of ordinary differential equations with algebraic constrains. Newton’s iteration is implemented with the developed methods to solve DAEs. The numerical results showed the performance of the developed methods is more efficient then existing methods in terms of maximum error and average error. In conclusion, the proposed one-step implicit hybrid methods are suitable for solving stiff ordinary differential equations and semi-explicit index-1 differential algebraic equations.
format	Thesis
qualification_level	Master's degree
author	Khoo, Kai Wen
author_facet	Khoo, Kai Wen
author_sort	Khoo, Kai Wen
title	Numerical solutions of stiff ordinary differential equations and differential algebraic equations using one-step implicit hybrid methods
title_short	Numerical solutions of stiff ordinary differential equations and differential algebraic equations using one-step implicit hybrid methods
title_full	Numerical solutions of stiff ordinary differential equations and differential algebraic equations using one-step implicit hybrid methods
title_fullStr	Numerical solutions of stiff ordinary differential equations and differential algebraic equations using one-step implicit hybrid methods
title_full_unstemmed	Numerical solutions of stiff ordinary differential equations and differential algebraic equations using one-step implicit hybrid methods
title_sort	numerical solutions of stiff ordinary differential equations and differential algebraic equations using one-step implicit hybrid methods
granting_institution	Universiti Putra Malaysia
publishDate	2015
url	http://psasir.upm.edu.my/id/eprint/58929/1/IPM%202015%2014IR.pdf
_version_	1747812226797928448

Numerical solutions of stiff ordinary differential equations and differential algebraic equations using one-step implicit hybrid methods

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