First order differential equation with piecewise constant argument

In recent years, differential equation with piecewise constant argument (DEPCA) have started to play crucial roles of the phenomena in the real world. There are many problems occurred involving piecewise constant arguments in the field of mathematics, science and engineering. However, behaviour of t...

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Main Author:	Ahmad, Mohd. Shahrullizam
Format:	Thesis
Language:	English
Published:	2020
Subjects:	QA Mathematics
Online Access:	http://eprints.utm.my/id/eprint/101782/1/MohdShahrullizamAhmadMFS2020.pdf.pdf
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id	my-utm-ep.101782
record_format	uketd_dc
spelling	my-utm-ep.1017822023-07-09T02:17:11Z First order differential equation with piecewise constant argument 2020 Ahmad, Mohd. Shahrullizam QA Mathematics In recent years, differential equation with piecewise constant argument (DEPCA) have started to play crucial roles of the phenomena in the real world. There are many problems occurred involving piecewise constant arguments in the field of mathematics, science and engineering. However, behaviour of the system with piecewise constant arguments is more complex when compared to the corresponding continuous regular systems. This study focused on solving first order nonlinear differential equations with piecewise constant argument. There are two types of differential equation which are the first order differential equation and the Bernoulli-type equations. The mathematical approaches are based on the DEPCA of simple forms, especially in the form of [t] to which a continuous system is considered directly over a unit interval. In order to solve these equations, the condition of existence and uniqueness are used to determine both the types of equations for some class functions of g. Thus, an explicit form of solutions for a certain class of Bernoulli-type equations was solved indirectly by using the previous approached. At the same time, the periodicity conditions for these solutions were established. Several examples were explained for both types of differential equation and some graphs were obtained by using MATHEMATICA software. 2020 Thesis http://eprints.utm.my/id/eprint/101782/ http://eprints.utm.my/id/eprint/101782/1/MohdShahrullizamAhmadMFS2020.pdf.pdf application/pdf en public http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:146271 masters Universiti Teknologi Malaysia Faculty of Science
institution	Universiti Teknologi Malaysia
collection	UTM Institutional Repository
language	English
topic	QA Mathematics
spellingShingle	QA Mathematics Ahmad, Mohd. Shahrullizam First order differential equation with piecewise constant argument
description	In recent years, differential equation with piecewise constant argument (DEPCA) have started to play crucial roles of the phenomena in the real world. There are many problems occurred involving piecewise constant arguments in the field of mathematics, science and engineering. However, behaviour of the system with piecewise constant arguments is more complex when compared to the corresponding continuous regular systems. This study focused on solving first order nonlinear differential equations with piecewise constant argument. There are two types of differential equation which are the first order differential equation and the Bernoulli-type equations. The mathematical approaches are based on the DEPCA of simple forms, especially in the form of [t] to which a continuous system is considered directly over a unit interval. In order to solve these equations, the condition of existence and uniqueness are used to determine both the types of equations for some class functions of g. Thus, an explicit form of solutions for a certain class of Bernoulli-type equations was solved indirectly by using the previous approached. At the same time, the periodicity conditions for these solutions were established. Several examples were explained for both types of differential equation and some graphs were obtained by using MATHEMATICA software.
format	Thesis
qualification_level	Master's degree
author	Ahmad, Mohd. Shahrullizam
author_facet	Ahmad, Mohd. Shahrullizam
author_sort	Ahmad, Mohd. Shahrullizam
title	First order differential equation with piecewise constant argument
title_short	First order differential equation with piecewise constant argument
title_full	First order differential equation with piecewise constant argument
title_fullStr	First order differential equation with piecewise constant argument
title_full_unstemmed	First order differential equation with piecewise constant argument
title_sort	first order differential equation with piecewise constant argument
granting_institution	Universiti Teknologi Malaysia
granting_department	Faculty of Science
publishDate	2020
url	http://eprints.utm.my/id/eprint/101782/1/MohdShahrullizamAhmadMFS2020.pdf.pdf
_version_	1776100770300559360

First order differential equation with piecewise constant argument

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