Staff View: The application of discrete homotopy analysis method in one-dimensional thermal problem

The application of discrete homotopy analysis method in one-dimensional thermal problem

Many engineering phenomena can be performed in mathematical modelling. Many thermal problems can be presented in Fredholm integral equation. A discretized version of Homotopy analysis method which introduced by Behiry et al (2010) is applied for solving the Fredholm integral equation. Besides that,...

Full description

Saved in:

Bibliographic Details
Main Author:	Ooi, Qian Fen
Format:	Thesis
Language:	English
Published:	2014
Subjects:	QA Mathematics
Online Access:	http://eprints.utm.my/id/eprint/48635/1/OoiQianFenMFS2014.pdf http://eprints.utm.my/id/eprint/48635/ http://dms.library.utm.my:8080/vital/access/manager/Repository?query=The+application+of+discrete+homotopy+analysis+method+in+one-dimensional+thermal+problem&queryType=vitalDismax&public=true
Tags:	Add Tag No Tags, Be the first to tag this record!

id	my.utm.48635
record_format	eprints
spelling	my.utm.486352020-03-05T02:52:04Z http://eprints.utm.my/id/eprint/48635/ The application of discrete homotopy analysis method in one-dimensional thermal problem Ooi, Qian Fen QA Mathematics Many engineering phenomena can be performed in mathematical modelling. Many thermal problems can be presented in Fredholm integral equation. A discretized version of Homotopy analysis method which introduced by Behiry et al (2010) is applied for solving the Fredholm integral equation. Besides that, we used a numerical method which is trapezoidal rule to solve the problem and make comparison with DHAM results. Comparison of approximation results from both methods demonstrates that DHAM is more accurate than trapezoidal rule as the DHAM convergent series solutions are well coincide with the exact solution. The convergence control parameter ℏ in DHAM is able to find the convergence region and control the convergence region of series solution. Moreover, DHAM can help to quicken the convergence of series solution. Therefore, DHAM is a powerful tool to solve the non-linear problem and can be applied to many others linear problems as well. Last but not least, DHAM is a good technique in solving non-linear problems in the science and engineering field. 2014 Thesis NonPeerReviewed application/pdf en http://eprints.utm.my/id/eprint/48635/1/OoiQianFenMFS2014.pdf Ooi, Qian Fen (2014) The application of discrete homotopy analysis method in one-dimensional thermal problem. Masters thesis, Universiti Teknologi Malaysia, Faculty of Science. http://dms.library.utm.my:8080/vital/access/manager/Repository?query=The+application+of+discrete+homotopy+analysis+method+in+one-dimensional+thermal+problem&queryType=vitalDismax&public=true
institution	Universiti Teknologi Malaysia
building	UTM Library
collection	Institutional Repository
continent	Asia
country	Malaysia
content_provider	Universiti Teknologi Malaysia
content_source	UTM Institutional Repository
url_provider	http://eprints.utm.my/
language	English
topic	QA Mathematics
spellingShingle	QA Mathematics Ooi, Qian Fen The application of discrete homotopy analysis method in one-dimensional thermal problem
description	Many engineering phenomena can be performed in mathematical modelling. Many thermal problems can be presented in Fredholm integral equation. A discretized version of Homotopy analysis method which introduced by Behiry et al (2010) is applied for solving the Fredholm integral equation. Besides that, we used a numerical method which is trapezoidal rule to solve the problem and make comparison with DHAM results. Comparison of approximation results from both methods demonstrates that DHAM is more accurate than trapezoidal rule as the DHAM convergent series solutions are well coincide with the exact solution. The convergence control parameter ℏ in DHAM is able to find the convergence region and control the convergence region of series solution. Moreover, DHAM can help to quicken the convergence of series solution. Therefore, DHAM is a powerful tool to solve the non-linear problem and can be applied to many others linear problems as well. Last but not least, DHAM is a good technique in solving non-linear problems in the science and engineering field.
format	Thesis
author	Ooi, Qian Fen
author_facet	Ooi, Qian Fen
author_sort	Ooi, Qian Fen
title	The application of discrete homotopy analysis method in one-dimensional thermal problem
title_short	The application of discrete homotopy analysis method in one-dimensional thermal problem
title_full	The application of discrete homotopy analysis method in one-dimensional thermal problem
title_fullStr	The application of discrete homotopy analysis method in one-dimensional thermal problem
title_full_unstemmed	The application of discrete homotopy analysis method in one-dimensional thermal problem
title_sort	application of discrete homotopy analysis method in one-dimensional thermal problem
publishDate	2014
url	http://eprints.utm.my/id/eprint/48635/1/OoiQianFenMFS2014.pdf http://eprints.utm.my/id/eprint/48635/ http://dms.library.utm.my:8080/vital/access/manager/Repository?query=The+application+of+discrete+homotopy+analysis+method+in+one-dimensional+thermal+problem&queryType=vitalDismax&public=true
_version_	1662754262499721216
score	13.211869

The application of discrete homotopy analysis method in one-dimensional thermal problem

Similar Items