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Solving Klein-Gordon Equation using Banach Contraction Method / Muhammad Akmal Yahya and Muhammad Alif Muzammil Mat Isa

The Klein-Gordon equation, often known as the Dirac Oscillator (DO), is one of the most infamous equations that has been applied in modern relativity quantum physics. The Sumudu Decomposition Method (SDM), Variational Iteration Method (VIM), Laplace Decomposition Method (LDM), Adomian Decomposition...

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Main Authors: Yahya, Muhammad Akmal, Mat Isa, Muhammad Alif Muzammil
Format: Student Project
Language:English
Published: 2023
Subjects:
Equations
Mathematical statistics. Probabilities
Online Access:https://ir.uitm.edu.my/id/eprint/82506/1/82506.pdf
https://ir.uitm.edu.my/id/eprint/82506/
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spelling my.uitm.ir.825062023-08-15T00:05:13Z https://ir.uitm.edu.my/id/eprint/82506/ Solving Klein-Gordon Equation using Banach Contraction Method / Muhammad Akmal Yahya and Muhammad Alif Muzammil Mat Isa Yahya, Muhammad Akmal Mat Isa, Muhammad Alif Muzammil Equations Mathematical statistics. Probabilities The Klein-Gordon equation, often known as the Dirac Oscillator (DO), is one of the most infamous equations that has been applied in modern relativity quantum physics. The Sumudu Decomposition Method (SDM), Variational Iteration Method (VIM), Laplace Decomposition Method (LDM), Adomian Decomposition Method (ADM), Homotopy Perturbation Method (HPM), and many other methods have been proposed in recent years to solve the Klein-Gordon equation. However, there are still some drawbacks to the nonlinear in these methods, particularly the nonlinear term is difficult and complex to compute. Therefore, Banach Contraction Method (BCM) will be utilised in this study to examine its accuracy whether it can be a new approach to solving the linear Klein-Gordon equation. Four cases of the linear Klein-Gordon equation were identified, and they were presented effectively in this report. All cases demonstrated that, as the iteration is increasing, the solution will be leading to the close form of the exact solution using BCM. Hence, the initial value problems of the Klein-Gordon equations are successfully solved using the BCM. Therefore, this study demonstrates that the BCM is more reliable and simpler when dealing with linear Klein-Gordon equation. As for recommendation, the researchers in the future can conduct a study on solving the nonlinear Klein-Gordon equation by using BCM. 2023 Student Project NonPeerReviewed text en https://ir.uitm.edu.my/id/eprint/82506/1/82506.pdf Solving Klein-Gordon Equation using Banach Contraction Method / Muhammad Akmal Yahya and Muhammad Alif Muzammil Mat Isa. (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 Equations
Mathematical statistics. Probabilities
spellingShingle Equations
Mathematical statistics. Probabilities
Yahya, Muhammad Akmal
Mat Isa, Muhammad Alif Muzammil
Solving Klein-Gordon Equation using Banach Contraction Method / Muhammad Akmal Yahya and Muhammad Alif Muzammil Mat Isa
description The Klein-Gordon equation, often known as the Dirac Oscillator (DO), is one of the most infamous equations that has been applied in modern relativity quantum physics. The Sumudu Decomposition Method (SDM), Variational Iteration Method (VIM), Laplace Decomposition Method (LDM), Adomian Decomposition Method (ADM), Homotopy Perturbation Method (HPM), and many other methods have been proposed in recent years to solve the Klein-Gordon equation. However, there are still some drawbacks to the nonlinear in these methods, particularly the nonlinear term is difficult and complex to compute. Therefore, Banach Contraction Method (BCM) will be utilised in this study to examine its accuracy whether it can be a new approach to solving the linear Klein-Gordon equation. Four cases of the linear Klein-Gordon equation were identified, and they were presented effectively in this report. All cases demonstrated that, as the iteration is increasing, the solution will be leading to the close form of the exact solution using BCM. Hence, the initial value problems of the Klein-Gordon equations are successfully solved using the BCM. Therefore, this study demonstrates that the BCM is more reliable and simpler when dealing with linear Klein-Gordon equation. As for recommendation, the researchers in the future can conduct a study on solving the nonlinear Klein-Gordon equation by using BCM.
format Student Project
author Yahya, Muhammad Akmal
Mat Isa, Muhammad Alif Muzammil
author_facet Yahya, Muhammad Akmal
Mat Isa, Muhammad Alif Muzammil
author_sort Yahya, Muhammad Akmal
title Solving Klein-Gordon Equation using Banach Contraction Method / Muhammad Akmal Yahya and Muhammad Alif Muzammil Mat Isa
title_short Solving Klein-Gordon Equation using Banach Contraction Method / Muhammad Akmal Yahya and Muhammad Alif Muzammil Mat Isa
title_full Solving Klein-Gordon Equation using Banach Contraction Method / Muhammad Akmal Yahya and Muhammad Alif Muzammil Mat Isa
title_fullStr Solving Klein-Gordon Equation using Banach Contraction Method / Muhammad Akmal Yahya and Muhammad Alif Muzammil Mat Isa
title_full_unstemmed Solving Klein-Gordon Equation using Banach Contraction Method / Muhammad Akmal Yahya and Muhammad Alif Muzammil Mat Isa
title_sort solving klein-gordon equation using banach contraction method / muhammad akmal yahya and muhammad alif muzammil mat isa
publishDate 2023
url https://ir.uitm.edu.my/id/eprint/82506/1/82506.pdf
https://ir.uitm.edu.my/id/eprint/82506/
_version_ 1775626453533065216
score 13.244368

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