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:	https://ir.uitm.edu.my/id/eprint/14332/1/14332.pdf
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id	my-uitm-ir.14332
record_format	uketd_dc
spelling	my-uitm-ir.143322022-04-01T03:30:45Z A new scheme for solving goursat problem using newton-cotes integration formula / Ros Fadilah Deraman 2014-05 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. 2014-05 Thesis https://ir.uitm.edu.my/id/eprint/14332/ https://ir.uitm.edu.my/id/eprint/14332/1/14332.pdf text en public mphil masters Universiti Teknologi MARA Faculty of Computer and Mathematical Sciences Nasir, Mohd Agos Salim (Dr.) Jayes, Mohd Idris (Assoc. Prof. Dr.) Awang Kechil, Seripah (Assoc. Prof. Dr.)
institution	Universiti Teknologi MARA
collection	UiTM Institutional Repository
language	English
advisor	Nasir, Mohd Agos Salim (Dr.) Jayes, Mohd Idris (Assoc. Prof. Dr.) Awang Kechil, Seripah (Assoc. Prof. Dr.)
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
qualification_name	Master of Philosophy (M.Phil.)
qualification_level	Master's degree
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
granting_institution	Universiti Teknologi MARA
granting_department	Faculty of Computer and Mathematical Sciences
publishDate	2014
url	https://ir.uitm.edu.my/id/eprint/14332/1/14332.pdf
_version_	1783733256376549376

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

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