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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主要作者: Ahmad, Mohd. Shahrullizam
格式: Thesis
語言:English
出版: 2020
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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