Classification of second order partial differential equation using maple and comparison for the solutions

The study of partial differential equations plays a significant role in many fields including mathematics, physics, and engineering. A partial differential equation (PDE) relates the partial derivatives of a function of two or more independent variables together. The general linear second order part...

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Main Author:	Algabishi, Ghadeer Omar S
Format:	Thesis
Language:	English
Published:	2015
Subjects:	Differential equations Partial
Online Access:	http://psasir.upm.edu.my/id/eprint/57072/1/FS%202015%209RR.pdf
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spelling	my-upm-ir.570722017-09-19T05:40:18Z Classification of second order partial differential equation using maple and comparison for the solutions 2015-06 Algabishi, Ghadeer Omar S The study of partial differential equations plays a significant role in many fields including mathematics, physics, and engineering. A partial differential equation (PDE) relates the partial derivatives of a function of two or more independent variables together. The general linear second order partial differential equation with constant coefficient has the form aZx x + bZx y +cZy y +dZx +eZy + f Z = g(x, y). There are many methods of solving this type of PDE’s such as finite elements, finite different and crank Nicolson depends on its classifications based on Z = b2-4ac. It is also well known that PDE is hyperbolic when -> 0, parabolic when - 0 and elliptic when-<0. In this research study, classification of the partial differential equation with constant coefficient is achieved by using Maple program. The classifications of variable coefficients of partial differential equations by Maple program are also given. The PDE’s after the convolution has the form AZx x + BZx y + CZy y + DZx + EZy + F Z = G, where A, B and C are coefficients of the PDE’s after the convolution. Further more the classification PDE’s with convolution are addressed by using -1=B2-4AC. Similarities in the classification of PDE’s before and after convolution were found. The solution of some important problems such as the wave equation is highly need of and occurs as one of three fundamental equations in mathematical physics that occurs in many branches of physics, applied mathematics, and engineering. In this research work, some problems of PDE’s with constant coefficient are solved by double Laplace transforms method. The same problems of the PDE’s are modified by some convolution function. The solutions of this new PDE’s are obtained by double Laplace transform. Graphical comparisons indicated that the methods are the same. In the same way, the PDE’s with variable coefficient are solved by double Laplace transforms methods. Then the same problem of the PDE’s is modified by some convolution functions. The new PDE’s are solved after convolution. However, graphical comparison made revealed that this two PDE’s before and after convolution are the same. Differential equations Partial 2015-06 Thesis http://psasir.upm.edu.my/id/eprint/57072/ http://psasir.upm.edu.my/id/eprint/57072/1/FS%202015%209RR.pdf application/pdf en public masters Universiti Putra Malaysia Differential equations Partial
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English
topic	Differential equations Partial
spellingShingle	Differential equations Partial Algabishi, Ghadeer Omar S Classification of second order partial differential equation using maple and comparison for the solutions
description	The study of partial differential equations plays a significant role in many fields including mathematics, physics, and engineering. A partial differential equation (PDE) relates the partial derivatives of a function of two or more independent variables together. The general linear second order partial differential equation with constant coefficient has the form aZx x + bZx y +cZy y +dZx +eZy + f Z = g(x, y). There are many methods of solving this type of PDE’s such as finite elements, finite different and crank Nicolson depends on its classifications based on Z = b2-4ac. It is also well known that PDE is hyperbolic when -> 0, parabolic when - 0 and elliptic when-<0. In this research study, classification of the partial differential equation with constant coefficient is achieved by using Maple program. The classifications of variable coefficients of partial differential equations by Maple program are also given. The PDE’s after the convolution has the form AZx x + BZx y + CZy y + DZx + EZy + F Z = G, where A, B and C are coefficients of the PDE’s after the convolution. Further more the classification PDE’s with convolution are addressed by using -1=B2-4AC. Similarities in the classification of PDE’s before and after convolution were found. The solution of some important problems such as the wave equation is highly need of and occurs as one of three fundamental equations in mathematical physics that occurs in many branches of physics, applied mathematics, and engineering. In this research work, some problems of PDE’s with constant coefficient are solved by double Laplace transforms method. The same problems of the PDE’s are modified by some convolution function. The solutions of this new PDE’s are obtained by double Laplace transform. Graphical comparisons indicated that the methods are the same. In the same way, the PDE’s with variable coefficient are solved by double Laplace transforms methods. Then the same problem of the PDE’s is modified by some convolution functions. The new PDE’s are solved after convolution. However, graphical comparison made revealed that this two PDE’s before and after convolution are the same.
format	Thesis
qualification_level	Master's degree
author	Algabishi, Ghadeer Omar S
author_facet	Algabishi, Ghadeer Omar S
author_sort	Algabishi, Ghadeer Omar S
title	Classification of second order partial differential equation using maple and comparison for the solutions
title_short	Classification of second order partial differential equation using maple and comparison for the solutions
title_full	Classification of second order partial differential equation using maple and comparison for the solutions
title_fullStr	Classification of second order partial differential equation using maple and comparison for the solutions
title_full_unstemmed	Classification of second order partial differential equation using maple and comparison for the solutions
title_sort	classification of second order partial differential equation using maple and comparison for the solutions
granting_institution	Universiti Putra Malaysia
publishDate	2015
url	http://psasir.upm.edu.my/id/eprint/57072/1/FS%202015%209RR.pdf
_version_	1747812162141683712

Classification of second order partial differential equation using maple and comparison for the solutions

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