Comparing chebyshev polynomials and adomian decomposition method in solving nonlinear volterra integral equations of second kind

The nonlinear integral equations are usually difficult to solve analytically and in many cases, it is required to obtain the approximate solutions. The nonlinear Volterra integral equation of second kind is one of them. This dissertation compares two methods that are used in order to solve nonlinear...

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Main Author:	Mohamad Sapawi, Siti Aminah
Format:	Thesis
Language:	English
Published:	2014
Subjects:	QA Mathematics
Online Access:	http://eprints.utm.my/id/eprint/51411/25/SitiAminahMohamadMFS2014.pdf
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id	my-utm-ep.51411
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spelling	my-utm-ep.514112020-07-13T03:53:41Z Comparing chebyshev polynomials and adomian decomposition method in solving nonlinear volterra integral equations of second kind 2014-06 Mohamad Sapawi, Siti Aminah QA Mathematics The nonlinear integral equations are usually difficult to solve analytically and in many cases, it is required to obtain the approximate solutions. The nonlinear Volterra integral equation of second kind is one of them. This dissertation compares two methods that are used in order to solve nonlinear Volterra integral equation of second kind. Those are Chebyshev polynomials and Adomian decomposition method. The Chebyshev polynomials are developed to approximate the solution of linear and nonlinear Volterra integral equations. While, Adomian decomposition method, is a method that can be applied directly for all type of linear and nonlinear integral equations and maintain high accuracy of numerical solution. Hence, the best method is picked based on the absolute error that will be compared with the exact solution. 2014-06 Thesis http://eprints.utm.my/id/eprint/51411/ http://eprints.utm.my/id/eprint/51411/25/SitiAminahMohamadMFS2014.pdf application/pdf en public http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:86516 masters 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 Mohamad Sapawi, Siti Aminah Comparing chebyshev polynomials and adomian decomposition method in solving nonlinear volterra integral equations of second kind
description	The nonlinear integral equations are usually difficult to solve analytically and in many cases, it is required to obtain the approximate solutions. The nonlinear Volterra integral equation of second kind is one of them. This dissertation compares two methods that are used in order to solve nonlinear Volterra integral equation of second kind. Those are Chebyshev polynomials and Adomian decomposition method. The Chebyshev polynomials are developed to approximate the solution of linear and nonlinear Volterra integral equations. While, Adomian decomposition method, is a method that can be applied directly for all type of linear and nonlinear integral equations and maintain high accuracy of numerical solution. Hence, the best method is picked based on the absolute error that will be compared with the exact solution.
format	Thesis
qualification_level	Master's degree
author	Mohamad Sapawi, Siti Aminah
author_facet	Mohamad Sapawi, Siti Aminah
author_sort	Mohamad Sapawi, Siti Aminah
title	Comparing chebyshev polynomials and adomian decomposition method in solving nonlinear volterra integral equations of second kind
title_short	Comparing chebyshev polynomials and adomian decomposition method in solving nonlinear volterra integral equations of second kind
title_full	Comparing chebyshev polynomials and adomian decomposition method in solving nonlinear volterra integral equations of second kind
title_fullStr	Comparing chebyshev polynomials and adomian decomposition method in solving nonlinear volterra integral equations of second kind
title_full_unstemmed	Comparing chebyshev polynomials and adomian decomposition method in solving nonlinear volterra integral equations of second kind
title_sort	comparing chebyshev polynomials and adomian decomposition method in solving nonlinear volterra integral equations of second kind
granting_institution	Universiti Teknologi Malaysia, Faculty of Science
granting_department	Faculty of Science
publishDate	2014
url	http://eprints.utm.my/id/eprint/51411/25/SitiAminahMohamadMFS2014.pdf
_version_	1747817548883165184

Comparing chebyshev polynomials and adomian decomposition method in solving nonlinear volterra integral equations of second kind

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