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Comparison of higher order iterative methods in solving nonlinear equations / Muhammad Syafiq Salleh

This study explores the effectiveness of five higher-order iterative techniques for solving nonlinear equations which are Newton method, Jarratt method, Frontini and Sormani method, Potra and Ptak method, and Weerakoon and Fernando method. All of these methods are the early improvement of the Newton...

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Main Author: Salleh, Muhammad Syafiq
Format: Thesis
Language:English
Published: 2024
Subjects:
Analytical methods used in the solution of physical problems
Online Access:https://ir.uitm.edu.my/id/eprint/106183/1/106183.pdf
https://ir.uitm.edu.my/id/eprint/106183/
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spelling my.uitm.ir.1061832024-11-30T22:55:42Z https://ir.uitm.edu.my/id/eprint/106183/ Comparison of higher order iterative methods in solving nonlinear equations / Muhammad Syafiq Salleh Salleh, Muhammad Syafiq Analytical methods used in the solution of physical problems This study explores the effectiveness of five higher-order iterative techniques for solving nonlinear equations which are Newton method, Jarratt method, Frontini and Sormani method, Potra and Ptak method, and Weerakoon and Fernando method. All of these methods are the early improvement of the Newton method. All these methods will be compared and test with eight different type of test functions and also with differences tolerance. The comparison of the methods is assessed according on the amount of CPU time used, the accuracy of the outcomes, and the number of iterations needed. According to the investigation, the Newton method approach is the most CPU-time efficient because of its simplicity, but the Jarratt method performs better with less repetitions because of its greater convergence rate. Most of the methods have similar accuracy, however the Potra and Ptak method exhibits more frequent convergence failures. This study emphasizes how important it is to balance iteration count and computational efficiency when choosing suitable iterative algorithms based on particular computational requirements. 2024 Thesis NonPeerReviewed text en https://ir.uitm.edu.my/id/eprint/106183/1/106183.pdf Comparison of higher order iterative methods in solving nonlinear equations / Muhammad Syafiq Salleh. (2024) Degree thesis, thesis, Universiti Teknologi MARA, Terengganu.
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 Analytical methods used in the solution of physical problems
spellingShingle Analytical methods used in the solution of physical problems
Salleh, Muhammad Syafiq
Comparison of higher order iterative methods in solving nonlinear equations / Muhammad Syafiq Salleh
description This study explores the effectiveness of five higher-order iterative techniques for solving nonlinear equations which are Newton method, Jarratt method, Frontini and Sormani method, Potra and Ptak method, and Weerakoon and Fernando method. All of these methods are the early improvement of the Newton method. All these methods will be compared and test with eight different type of test functions and also with differences tolerance. The comparison of the methods is assessed according on the amount of CPU time used, the accuracy of the outcomes, and the number of iterations needed. According to the investigation, the Newton method approach is the most CPU-time efficient because of its simplicity, but the Jarratt method performs better with less repetitions because of its greater convergence rate. Most of the methods have similar accuracy, however the Potra and Ptak method exhibits more frequent convergence failures. This study emphasizes how important it is to balance iteration count and computational efficiency when choosing suitable iterative algorithms based on particular computational requirements.
format Thesis
author Salleh, Muhammad Syafiq
author_facet Salleh, Muhammad Syafiq
author_sort Salleh, Muhammad Syafiq
title Comparison of higher order iterative methods in solving nonlinear equations / Muhammad Syafiq Salleh
title_short Comparison of higher order iterative methods in solving nonlinear equations / Muhammad Syafiq Salleh
title_full Comparison of higher order iterative methods in solving nonlinear equations / Muhammad Syafiq Salleh
title_fullStr Comparison of higher order iterative methods in solving nonlinear equations / Muhammad Syafiq Salleh
title_full_unstemmed Comparison of higher order iterative methods in solving nonlinear equations / Muhammad Syafiq Salleh
title_sort comparison of higher order iterative methods in solving nonlinear equations / muhammad syafiq salleh
publishDate 2024
url https://ir.uitm.edu.my/id/eprint/106183/1/106183.pdf
https://ir.uitm.edu.my/id/eprint/106183/
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score 13.222552

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