Discrete homotopy analysis method on heat conduction with radiation problem via fredholm integral equation

Science and engineering problems can be modelled in Fredholm integral equations (FIE) whether it is a linear or nonlinear problem. There is method called homotopy analysis method (HAM) can be used to solve even highly nonlinear equations ensuring convergence by introducing convergence control parame...

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Main Author:	A. Rahman, Muhammad Farid
Format:	Thesis
Language:	English
Published:	2019
Subjects:	QA Mathematics
Online Access:	http://eprints.utm.my/id/eprint/102172/1/MuhammadFaridARahmanMFS2019.pdf.pdf
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id	my-utm-ep.102172
record_format	uketd_dc
spelling	my-utm-ep.1021722023-08-07T08:25:40Z Discrete homotopy analysis method on heat conduction with radiation problem via fredholm integral equation 2019 A. Rahman, Muhammad Farid QA Mathematics Science and engineering problems can be modelled in Fredholm integral equations (FIE) whether it is a linear or nonlinear problem. There is method called homotopy analysis method (HAM) can be used to solve even highly nonlinear equations ensuring convergence by introducing convergence control parameter, ?. HAM has been applied to solve linear and nonlinear Fredholm integral equations with high accuracy. There is also discretized version of HAM which evaluate definite integrals in FIE using numerical integration method which is called discrete Homotopy analysis method (DHAM). We applied DHAM on highly nonlinear Fredholm integral equation and compared the results with Nystrom method. It shows that convergence control parameter, ? introduced in DHAM provides a convenient way of ensuring convergent series solutions. DHAM convergence is also faster than Nystrom method in solving nonlinear equations. We proved that accuracy of both DHAM and Nystrom method are dependent on numerical integration. Therefore, the DHAM is superior than Nystrom method in solving nonlinear Fredholm integral equations. 2019 Thesis http://eprints.utm.my/id/eprint/102172/ http://eprints.utm.my/id/eprint/102172/1/MuhammadFaridARahmanMFS2019.pdf.pdf application/pdf en public http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:146248 masters Universiti Teknologi Malaysia Faculty of Science
institution	Universiti Teknologi Malaysia
collection	UTM Institutional Repository
language	English
topic	QA Mathematics
spellingShingle	QA Mathematics A. Rahman, Muhammad Farid Discrete homotopy analysis method on heat conduction with radiation problem via fredholm integral equation
description	Science and engineering problems can be modelled in Fredholm integral equations (FIE) whether it is a linear or nonlinear problem. There is method called homotopy analysis method (HAM) can be used to solve even highly nonlinear equations ensuring convergence by introducing convergence control parameter, ?. HAM has been applied to solve linear and nonlinear Fredholm integral equations with high accuracy. There is also discretized version of HAM which evaluate definite integrals in FIE using numerical integration method which is called discrete Homotopy analysis method (DHAM). We applied DHAM on highly nonlinear Fredholm integral equation and compared the results with Nystrom method. It shows that convergence control parameter, ? introduced in DHAM provides a convenient way of ensuring convergent series solutions. DHAM convergence is also faster than Nystrom method in solving nonlinear equations. We proved that accuracy of both DHAM and Nystrom method are dependent on numerical integration. Therefore, the DHAM is superior than Nystrom method in solving nonlinear Fredholm integral equations.
format	Thesis
qualification_level	Master's degree
author	A. Rahman, Muhammad Farid
author_facet	A. Rahman, Muhammad Farid
author_sort	A. Rahman, Muhammad Farid
title	Discrete homotopy analysis method on heat conduction with radiation problem via fredholm integral equation
title_short	Discrete homotopy analysis method on heat conduction with radiation problem via fredholm integral equation
title_full	Discrete homotopy analysis method on heat conduction with radiation problem via fredholm integral equation
title_fullStr	Discrete homotopy analysis method on heat conduction with radiation problem via fredholm integral equation
title_full_unstemmed	Discrete homotopy analysis method on heat conduction with radiation problem via fredholm integral equation
title_sort	discrete homotopy analysis method on heat conduction with radiation problem via fredholm integral equation
granting_institution	Universiti Teknologi Malaysia
granting_department	Faculty of Science
publishDate	2019
url	http://eprints.utm.my/id/eprint/102172/1/MuhammadFaridARahmanMFS2019.pdf.pdf
_version_	1776100863046057984

Discrete homotopy analysis method on heat conduction with radiation problem via fredholm integral equation

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