Solving nonlinear equations using Shah and Noor’s iterative method / Iman Muneera Zailani

Numerical root finding is the technique of approximating the roots of an equation through numerical methods. Numerical method is often chosen for solving nonlinear functions rather than analytical approach. The main purpose of this project is to compare the numerical methods chosen which are Newton’...

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Main Author:	Zailani, Iman Muneera
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/106178/1/106178.pdf
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id	my-uitm-ir.106178
record_format	uketd_dc
spelling	my-uitm-ir.1061782024-11-30T22:55:59Z Solving nonlinear equations using Shah and Noor’s iterative method / Iman Muneera Zailani 2024 Zailani, Iman Muneera Analytical methods used in the solution of physical problems Numerical root finding is the technique of approximating the roots of an equation through numerical methods. Numerical method is often chosen for solving nonlinear functions rather than analytical approach. The main purpose of this project is to compare the numerical methods chosen which are Newton’s method, Steffensen’s method, Shah and Noor’s First method, and Shah and Noor’s Second method to see which one is best for solving eight nonlinear functions, using Maple software, from four different types of functions which are trigonometric function, exponential function, quadratic function, and polynomial function using four different initial values with three stopping criteria. This is done by running programming code, based on the methods chosen, using Maple software. The comparison is based on the number of iterations, CPU time, and accuracy. The results via performance profile using SigmaPlot show that Newton’s method is overall the best method for all the criteria for its high level of efficiency and robustness. Both Shah and Noor’s First method and Shah and Noor’s Second method show comparable results with each other while Steffensen’s method shows the worst performance. 2024 Thesis https://ir.uitm.edu.my/id/eprint/106178/ https://ir.uitm.edu.my/id/eprint/106178/1/106178.pdf text en public degree Universiti Teknologi MARA, Terengganu College of Computing, Informatics and Mathematics Mohd Ali, Mohd Rivaie
institution	Universiti Teknologi MARA
collection	UiTM Institutional Repository
language	English
advisor	Mohd Ali, Mohd Rivaie
topic	Analytical methods used in the solution of physical problems
spellingShingle	Analytical methods used in the solution of physical problems Zailani, Iman Muneera Solving nonlinear equations using Shah and Noor’s iterative method / Iman Muneera Zailani
description	Numerical root finding is the technique of approximating the roots of an equation through numerical methods. Numerical method is often chosen for solving nonlinear functions rather than analytical approach. The main purpose of this project is to compare the numerical methods chosen which are Newton’s method, Steffensen’s method, Shah and Noor’s First method, and Shah and Noor’s Second method to see which one is best for solving eight nonlinear functions, using Maple software, from four different types of functions which are trigonometric function, exponential function, quadratic function, and polynomial function using four different initial values with three stopping criteria. This is done by running programming code, based on the methods chosen, using Maple software. The comparison is based on the number of iterations, CPU time, and accuracy. The results via performance profile using SigmaPlot show that Newton’s method is overall the best method for all the criteria for its high level of efficiency and robustness. Both Shah and Noor’s First method and Shah and Noor’s Second method show comparable results with each other while Steffensen’s method shows the worst performance.
format	Thesis
qualification_level	Bachelor degree
author	Zailani, Iman Muneera
author_facet	Zailani, Iman Muneera
author_sort	Zailani, Iman Muneera
title	Solving nonlinear equations using Shah and Noor’s iterative method / Iman Muneera Zailani
title_short	Solving nonlinear equations using Shah and Noor’s iterative method / Iman Muneera Zailani
title_full	Solving nonlinear equations using Shah and Noor’s iterative method / Iman Muneera Zailani
title_fullStr	Solving nonlinear equations using Shah and Noor’s iterative method / Iman Muneera Zailani
title_full_unstemmed	Solving nonlinear equations using Shah and Noor’s iterative method / Iman Muneera Zailani
title_sort	solving nonlinear equations using shah and noor’s iterative method / iman muneera zailani
granting_institution	Universiti Teknologi MARA, Terengganu
granting_department	College of Computing, Informatics and Mathematics
publishDate	2024
url	https://ir.uitm.edu.my/id/eprint/106178/1/106178.pdf
_version_	1818588169178710016

Solving nonlinear equations using Shah and Noor’s iterative method / Iman Muneera Zailani

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