A new scheme for solving goursat problem using newton-cotes integration formula / Ros Fadilah Deraman

The Goursat partial differential equation is a hyperbolic partial differential equation which arises in science and engineering fields. Many approaches have been suggested to approximate the solutions of the Goursat partial differential equations such as the finite difference method, Runge-Kutta met...

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Main Author:	Deraman, Ros Fadilah
Format:	Thesis
Language:	English
Published:	2014
Subjects:	Differential equations. Runge-Kutta formulas Partial differential equations (first order)
Online Access:	http://ir.uitm.edu.my/id/eprint/14332/ http://ir.uitm.edu.my/id/eprint/14332/1/TM_ROS%20FADILAH%20DERAMAN%20CS%2014_5.pdf

id	uitm-14332
recordtype	eprints
spelling	uitm-143322016-08-23T02:37:38Z http://ir.uitm.edu.my/id/eprint/14332/ A new scheme for solving goursat problem using newton-cotes integration formula / Ros Fadilah Deraman Deraman, Ros Fadilah Differential equations. Runge-Kutta formulas Partial differential equations (first order) The Goursat partial differential equation is a hyperbolic partial differential equation which arises in science and engineering fields. Many approaches have been suggested to approximate the solutions of the Goursat partial differential equations such as the finite difference method, Runge-Kutta method, differential transform method, variational iteration method and homotopy analysis method. These methods focus on series expansion and numerical differentiation approaches including the forward and central differences in deriving the schemes. In this thesis, we developed new schemes to solve a class of Goursat partial differential equations that applies the Newton-Cotes formula for approximating the double integrals terms. The Newton-Cotes numerical integration involves Newton-Cotes order one, Newton-Cotes order two, Newton-Cotes order three and Newton-Cotes order four. The linear and nonlinear homogeneous and inhomogeneous Goursat problems are examined. The new schemes gave quantitatively reliable results for the problems considered. The numerical analysis test has been performed to ensure that the new schemes are accurate, consistent, stable and converge in solving these problems. The accuracy level of the results obtained indicates the superiority of these new schemes over established scheme. It is also proven that the linear and nonlinear schemes are successfully converge to the exact solution. Thus, it implies that the schemes are also consistent and stable for linear and nonlinear Goursat problemsThe Goursat partial differential equation is a hyperbolic partial differential equation which arises in science and engineering fields. Many approaches have been suggested to approximate the solutions of the Goursat partial differential equations such as the finite difference method, Runge-Kutta method, differential transform method, variational iteration method and homotopy analysis method. These methods focus on series expansion and numerical differentiation approaches including the forward and central differences in deriving the schemes. In this thesis, we developed new schemes to solve a class of Goursat partial differential equations that applies the Newton-Cotes formula for approximating the double integrals terms. The Newton-Cotes numerical integration involves Newton-Cotes order one, Newton-Cotes order two, Newton-Cotes order three and Newton-Cotes order four. The linear and nonlinear homogeneous and inhomogeneous Goursat problems are examined. The new schemes gave quantitatively reliable results for the problems considered. The numerical analysis test has been performed to ensure that the new schemes are accurate, consistent, stable and converge in solving these problems. The accuracy level of the results obtained indicates the superiority of these new schemes over established scheme. It is also proven that the linear and nonlinear schemes are successfully converge to the exact solution. Thus, it implies that the schemes are also consistent and stable for linear and nonlinear Goursat problems 2014 Thesis NonPeerReviewed text en http://ir.uitm.edu.my/id/eprint/14332/1/TM_ROS%20FADILAH%20DERAMAN%20CS%2014_5.pdf Deraman, Ros Fadilah (2014) A new scheme for solving goursat problem using newton-cotes integration formula / Ros Fadilah Deraman. Masters thesis, Universiti Teknologi MARA.
repository_type	Digital Repository
institution_category	Local University
institution	Universiti Teknologi MARA
building	UiTM Institutional Repository
collection	Online Access
language	English
topic	Differential equations. Runge-Kutta formulas Partial differential equations (first order)
spellingShingle	Differential equations. Runge-Kutta formulas Partial differential equations (first order) Deraman, Ros Fadilah A new scheme for solving goursat problem using newton-cotes integration formula / Ros Fadilah Deraman
description	The Goursat partial differential equation is a hyperbolic partial differential equation which arises in science and engineering fields. Many approaches have been suggested to approximate the solutions of the Goursat partial differential equations such as the finite difference method, Runge-Kutta method, differential transform method, variational iteration method and homotopy analysis method. These methods focus on series expansion and numerical differentiation approaches including the forward and central differences in deriving the schemes. In this thesis, we developed new schemes to solve a class of Goursat partial differential equations that applies the Newton-Cotes formula for approximating the double integrals terms. The Newton-Cotes numerical integration involves Newton-Cotes order one, Newton-Cotes order two, Newton-Cotes order three and Newton-Cotes order four. The linear and nonlinear homogeneous and inhomogeneous Goursat problems are examined. The new schemes gave quantitatively reliable results for the problems considered. The numerical analysis test has been performed to ensure that the new schemes are accurate, consistent, stable and converge in solving these problems. The accuracy level of the results obtained indicates the superiority of these new schemes over established scheme. It is also proven that the linear and nonlinear schemes are successfully converge to the exact solution. Thus, it implies that the schemes are also consistent and stable for linear and nonlinear Goursat problemsThe Goursat partial differential equation is a hyperbolic partial differential equation which arises in science and engineering fields. Many approaches have been suggested to approximate the solutions of the Goursat partial differential equations such as the finite difference method, Runge-Kutta method, differential transform method, variational iteration method and homotopy analysis method. These methods focus on series expansion and numerical differentiation approaches including the forward and central differences in deriving the schemes. In this thesis, we developed new schemes to solve a class of Goursat partial differential equations that applies the Newton-Cotes formula for approximating the double integrals terms. The Newton-Cotes numerical integration involves Newton-Cotes order one, Newton-Cotes order two, Newton-Cotes order three and Newton-Cotes order four. The linear and nonlinear homogeneous and inhomogeneous Goursat problems are examined. The new schemes gave quantitatively reliable results for the problems considered. The numerical analysis test has been performed to ensure that the new schemes are accurate, consistent, stable and converge in solving these problems. The accuracy level of the results obtained indicates the superiority of these new schemes over established scheme. It is also proven that the linear and nonlinear schemes are successfully converge to the exact solution. Thus, it implies that the schemes are also consistent and stable for linear and nonlinear Goursat problems
format	Thesis
author	Deraman, Ros Fadilah
author_facet	Deraman, Ros Fadilah
author_sort	Deraman, Ros Fadilah
title	A new scheme for solving goursat problem using newton-cotes integration formula / Ros Fadilah Deraman
title_short	A new scheme for solving goursat problem using newton-cotes integration formula / Ros Fadilah Deraman
title_full	A new scheme for solving goursat problem using newton-cotes integration formula / Ros Fadilah Deraman
title_fullStr	A new scheme for solving goursat problem using newton-cotes integration formula / Ros Fadilah Deraman
title_full_unstemmed	A new scheme for solving goursat problem using newton-cotes integration formula / Ros Fadilah Deraman
title_sort	new scheme for solving goursat problem using newton-cotes integration formula / ros fadilah deraman
publishDate	2014
url	http://ir.uitm.edu.my/id/eprint/14332/ http://ir.uitm.edu.my/id/eprint/14332/1/TM_ROS%20FADILAH%20DERAMAN%20CS%2014_5.pdf
first_indexed	2023-09-18T22:51:23Z
last_indexed	2023-09-18T22:51:23Z
_version_	1777417567122489344

A new scheme for solving goursat problem using newton-cotes integration formula / Ros Fadilah Deraman

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