Discrete adomian decomposition method for solving fredholm integral equations of the second kind

The nonlinear Fredholm integral equation (FIE) represents a large amount of nonlinear phenomena that usually produces a considerable amount of difficulties. This dissertation will display some methods used for solving this problem, such as an Adomian Decomposition Method (ADM) which is based on deco...

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Main Author:	Mohammed, Salar Hameed
Format:	Thesis
Language:	English
Published:	2013
Subjects:	QA Mathematics
Online Access:	http://eprints.utm.my/id/eprint/47943/25/SalarHameedMohammedMFS2013.pdf
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spelling	my-utm-ep.479432017-07-17T04:24:08Z Discrete adomian decomposition method for solving fredholm integral equations of the second kind 2013-06 Mohammed, Salar Hameed QA Mathematics The nonlinear Fredholm integral equation (FIE) represents a large amount of nonlinear phenomena that usually produces a considerable amount of difficulties. This dissertation will display some methods used for solving this problem, such as an Adomian Decomposition Method (ADM) which is based on decomposing the solution to infinite series and numerical implementation of ADM for the special case when the kernel is separable. In addition, it discusses the process of applying the Discrete Adomian Decomposition Method (DADM) which gives the numerical solution at the nodes using quadrature rules like Simpsons rule and trapezoidal rule. The comparison of DADM with of both rules with the exact solution also are given. Furthermore the results from DADM, Triangles orthogonal functions (Tfs) and Rationalized Haar function (RHf) for two dimensional linear and nonlinear FIE of the second kind respectively are compared with exact solution. Hence the results obtained show equivalent accuracy when linear FIE of the second kind for two dimension were solved by DADM with Simpson’s rule and by Tfs. Whereas the results show of DADM with Simpson’s rule is more accurate than RHf to solve nonlinear FIE of the second kind for 2-D. 2013-06 Thesis http://eprints.utm.my/id/eprint/47943/ http://eprints.utm.my/id/eprint/47943/25/SalarHameedMohammedMFS2013.pdf application/pdf en public 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 Mohammed, Salar Hameed Discrete adomian decomposition method for solving fredholm integral equations of the second kind
description	The nonlinear Fredholm integral equation (FIE) represents a large amount of nonlinear phenomena that usually produces a considerable amount of difficulties. This dissertation will display some methods used for solving this problem, such as an Adomian Decomposition Method (ADM) which is based on decomposing the solution to infinite series and numerical implementation of ADM for the special case when the kernel is separable. In addition, it discusses the process of applying the Discrete Adomian Decomposition Method (DADM) which gives the numerical solution at the nodes using quadrature rules like Simpsons rule and trapezoidal rule. The comparison of DADM with of both rules with the exact solution also are given. Furthermore the results from DADM, Triangles orthogonal functions (Tfs) and Rationalized Haar function (RHf) for two dimensional linear and nonlinear FIE of the second kind respectively are compared with exact solution. Hence the results obtained show equivalent accuracy when linear FIE of the second kind for two dimension were solved by DADM with Simpson’s rule and by Tfs. Whereas the results show of DADM with Simpson’s rule is more accurate than RHf to solve nonlinear FIE of the second kind for 2-D.
format	Thesis
qualification_level	Master's degree
author	Mohammed, Salar Hameed
author_facet	Mohammed, Salar Hameed
author_sort	Mohammed, Salar Hameed
title	Discrete adomian decomposition method for solving fredholm integral equations of the second kind
title_short	Discrete adomian decomposition method for solving fredholm integral equations of the second kind
title_full	Discrete adomian decomposition method for solving fredholm integral equations of the second kind
title_fullStr	Discrete adomian decomposition method for solving fredholm integral equations of the second kind
title_full_unstemmed	Discrete adomian decomposition method for solving fredholm integral equations of the second kind
title_sort	discrete adomian decomposition method for solving fredholm integral equations of the second kind
granting_institution	Universiti Teknologi Malaysia, Faculty of Science
granting_department	Faculty of Science
publishDate	2013
url	http://eprints.utm.my/id/eprint/47943/25/SalarHameedMohammedMFS2013.pdf
_version_	1747817269409349632

Discrete adomian decomposition method for solving fredholm integral equations of the second kind

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