Laplace transform and adomian decomposition methods for solving nonlinear volterra integro-differential equations

Since its introduction in the 1980s, the Adomian Decomposition Method (ADM) has proven to be an efficient and reliable method for solving many types of problems. Originally developed to solve nonlinear functional equations, the ADM has since been used for a wide range of equation types (like boundar...

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Main Author:	Vafaeifar, Zahra
Format:	Thesis
Language:	English
Published:	2013
Subjects:	QA Mathematics
Online Access:	http://eprints.utm.my/id/eprint/41672/4/ZahraVafaeifarMFS2013REF.pdf
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id	my-utm-ep.41672
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spelling	my-utm-ep.416722017-06-22T01:15:59Z Laplace transform and adomian decomposition methods for solving nonlinear volterra integro-differential equations 2013-10 Vafaeifar, Zahra QA Mathematics Since its introduction in the 1980s, the Adomian Decomposition Method (ADM) has proven to be an efficient and reliable method for solving many types of problems. Originally developed to solve nonlinear functional equations, the ADM has since been used for a wide range of equation types (like boundary value problems, integral equations, equations arising in flow of incompressible and compressible fluids etc...). This work is devoted to an evaluation of the effectiveness of this method when used for solve nonlinear Volterra integro-differential equations and also the combined form of the Laplace transform method with the Adomian decomposition method is effectively and useful way to develop an analytic treatment for many types of equations, linear and nonlinear ordinary differential equations (ODE), linear and nonlinear partial differential equations (PDE). In this study will combined Laplace transform-Adomian decomposition method to solve nonlinear Volterra integro-differential equations, this study is divided into five Chapters. The first chapter is devoted to an introduction, the second is devoted to the literature review, and Chapter 3 devoted to research methodology, Chapter 4 presents the solution for the nonlinear Volterra integro-differential equation. Finally, the Chapter 5 is devoted to the conclusion and recommendations based on this study. 2013-10 Thesis http://eprints.utm.my/id/eprint/41672/ http://eprints.utm.my/id/eprint/41672/4/ZahraVafaeifarMFS2013REF.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 Vafaeifar, Zahra Laplace transform and adomian decomposition methods for solving nonlinear volterra integro-differential equations
description	Since its introduction in the 1980s, the Adomian Decomposition Method (ADM) has proven to be an efficient and reliable method for solving many types of problems. Originally developed to solve nonlinear functional equations, the ADM has since been used for a wide range of equation types (like boundary value problems, integral equations, equations arising in flow of incompressible and compressible fluids etc...). This work is devoted to an evaluation of the effectiveness of this method when used for solve nonlinear Volterra integro-differential equations and also the combined form of the Laplace transform method with the Adomian decomposition method is effectively and useful way to develop an analytic treatment for many types of equations, linear and nonlinear ordinary differential equations (ODE), linear and nonlinear partial differential equations (PDE). In this study will combined Laplace transform-Adomian decomposition method to solve nonlinear Volterra integro-differential equations, this study is divided into five Chapters. The first chapter is devoted to an introduction, the second is devoted to the literature review, and Chapter 3 devoted to research methodology, Chapter 4 presents the solution for the nonlinear Volterra integro-differential equation. Finally, the Chapter 5 is devoted to the conclusion and recommendations based on this study.
format	Thesis
qualification_level	Master's degree
author	Vafaeifar, Zahra
author_facet	Vafaeifar, Zahra
author_sort	Vafaeifar, Zahra
title	Laplace transform and adomian decomposition methods for solving nonlinear volterra integro-differential equations
title_short	Laplace transform and adomian decomposition methods for solving nonlinear volterra integro-differential equations
title_full	Laplace transform and adomian decomposition methods for solving nonlinear volterra integro-differential equations
title_fullStr	Laplace transform and adomian decomposition methods for solving nonlinear volterra integro-differential equations
title_full_unstemmed	Laplace transform and adomian decomposition methods for solving nonlinear volterra integro-differential equations
title_sort	laplace transform and adomian decomposition methods for solving nonlinear volterra integro-differential equations
granting_institution	Universiti Teknologi Malaysia, Faculty of Science
granting_department	Faculty of Science
publishDate	2013
url	http://eprints.utm.my/id/eprint/41672/4/ZahraVafaeifarMFS2013REF.pdf
_version_	1747816594532204544

Laplace transform and adomian decomposition methods for solving nonlinear volterra integro-differential equations

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