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Solving VAN der Pol equation using Banach Contraction Method / Hambali Kamarol Shaharim

The Van der Pol equation is a second-order nonlinear differential equation that can be found in a variety of domains such as electronics, biology, and physics. The equation describes the behaviour of a circuit that includes a nonlinear device known as a Van der Pol oscillator that shows limit cycle...

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Main Author: Kamarol Shaharim, Hambali
Format: Student Project
Language:English
Published: 2023
Subjects:
Dissertations, Academic. Preparation of theses
Online Access:https://ir.uitm.edu.my/id/eprint/93940/1/93940.pdf
https://ir.uitm.edu.my/id/eprint/93940/
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spelling my.uitm.ir.939402024-04-25T03:45:47Z https://ir.uitm.edu.my/id/eprint/93940/ Solving VAN der Pol equation using Banach Contraction Method / Hambali Kamarol Shaharim Kamarol Shaharim, Hambali Dissertations, Academic. Preparation of theses The Van der Pol equation is a second-order nonlinear differential equation that can be found in a variety of domains such as electronics, biology, and physics. The equation describes the behaviour of a circuit that includes a nonlinear device known as a Van der Pol oscillator that shows limit cycle oscillations. The Modification of Variational Iteration Method (MVIM), He's Parameter-Expanding Methods (HPEM), Adomian's Decomposition Method (ADM), Iteration Perturbation Method (IPM), Modified Adomian Decomposition Method (MADM), Perturbation Method (PM), and there are variety method have been suggested in recent years to solve Van der Pol equation. Nonetheless, despite its ubiquitous use, the Van der Pol oscillator's behaviour remains poorly understood in many circumstances, posing several hurdles for academics. Then, BCM will be applied in this study to check its efficiency whether it can be a new method to solving the nonlinear Van der Pol equation. Four nonlinear Van der Pol equation cases were identified and in this report they were presented adequately. All cases demonstrated that, as the iteration is increasing, the solution will be leading to the close form of the exact solution using BCM. Then, the Van der Pol equations initial value problems are satisfied in solved using the BCM. Hence, this study illustrates that the BCM is more dependable and straightforward when dealing with nonlinear Van der Pol equation. In the future, researchers could do a study deeply on solving the nonlinear Van der Pol equation using BCM so that BCM can use spreadly. 2023 Student Project NonPeerReviewed text en https://ir.uitm.edu.my/id/eprint/93940/1/93940.pdf Solving VAN der Pol equation using Banach Contraction Method / Hambali Kamarol Shaharim. (2023) [Student Project] (Unpublished)
institution Universiti Teknologi Mara
building Tun Abdul Razak Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Teknologi Mara
content_source UiTM Institutional Repository
url_provider http://ir.uitm.edu.my/
language English
topic Dissertations, Academic. Preparation of theses
spellingShingle Dissertations, Academic. Preparation of theses
Kamarol Shaharim, Hambali
Solving VAN der Pol equation using Banach Contraction Method / Hambali Kamarol Shaharim
description The Van der Pol equation is a second-order nonlinear differential equation that can be found in a variety of domains such as electronics, biology, and physics. The equation describes the behaviour of a circuit that includes a nonlinear device known as a Van der Pol oscillator that shows limit cycle oscillations. The Modification of Variational Iteration Method (MVIM), He's Parameter-Expanding Methods (HPEM), Adomian's Decomposition Method (ADM), Iteration Perturbation Method (IPM), Modified Adomian Decomposition Method (MADM), Perturbation Method (PM), and there are variety method have been suggested in recent years to solve Van der Pol equation. Nonetheless, despite its ubiquitous use, the Van der Pol oscillator's behaviour remains poorly understood in many circumstances, posing several hurdles for academics. Then, BCM will be applied in this study to check its efficiency whether it can be a new method to solving the nonlinear Van der Pol equation. Four nonlinear Van der Pol equation cases were identified and in this report they were presented adequately. All cases demonstrated that, as the iteration is increasing, the solution will be leading to the close form of the exact solution using BCM. Then, the Van der Pol equations initial value problems are satisfied in solved using the BCM. Hence, this study illustrates that the BCM is more dependable and straightforward when dealing with nonlinear Van der Pol equation. In the future, researchers could do a study deeply on solving the nonlinear Van der Pol equation using BCM so that BCM can use spreadly.
format Student Project
author Kamarol Shaharim, Hambali
author_facet Kamarol Shaharim, Hambali
author_sort Kamarol Shaharim, Hambali
title Solving VAN der Pol equation using Banach Contraction Method / Hambali Kamarol Shaharim
title_short Solving VAN der Pol equation using Banach Contraction Method / Hambali Kamarol Shaharim
title_full Solving VAN der Pol equation using Banach Contraction Method / Hambali Kamarol Shaharim
title_fullStr Solving VAN der Pol equation using Banach Contraction Method / Hambali Kamarol Shaharim
title_full_unstemmed Solving VAN der Pol equation using Banach Contraction Method / Hambali Kamarol Shaharim
title_sort solving van der pol equation using banach contraction method / hambali kamarol shaharim
publishDate 2023
url https://ir.uitm.edu.my/id/eprint/93940/1/93940.pdf
https://ir.uitm.edu.my/id/eprint/93940/
_version_ 1797926441109684224
score 13.211869

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