Application of air pollution data in Klang, Selangor to find multiple roots / Nurlaila Azwa Khamsani

Many types of methods such as Halley’s and super-Halley method, modified Newton’s method, and Schroder’s method can be used in finding multiple roots of nonlinear equations. Some methods cannot be used for finding multiple roots such as Newton’s method, Bisection method, Secant method, Muller’s meth...

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Main Author:	Khamsani, Nurlaila Azwa
Format:	Thesis
Language:	English
Published:	2023
Subjects:	Analytical methods used in the solution of physical problems
Online Access:	https://ir.uitm.edu.my/id/eprint/97760/1/97760.pdf
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id	my-uitm-ir.97760
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spelling	my-uitm-ir.977602024-07-27T17:58:23Z Application of air pollution data in Klang, Selangor to find multiple roots / Nurlaila Azwa Khamsani 2023 Khamsani, Nurlaila Azwa Analytical methods used in the solution of physical problems Many types of methods such as Halley’s and super-Halley method, modified Newton’s method, and Schroder’s method can be used in finding multiple roots of nonlinear equations. Some methods cannot be used for finding multiple roots such as Newton’s method, Bisection method, Secant method, Muller’s method, and many more. Thus, the modifications of some methods did by few researchers. This project will find the month that has highest value of mean concentration of PM10 and PM2.5 with the value of concentrations. Next, this project will be implementing the highest mean concentrations of particulate matter which are PM10 and PM2.5 in Klang as the initial guesses for finding multiple roots. Lastly, every function with different initial guess has its own best method by identifying the smallest error and smallest CPU time. For Modified Newton’s method, it is best to use on function (e-x2 — ex2 — x8 + 10)30 with initial guess 33.41. For Method 1 (M1), it is best to use on function (e-x2 — ex2 — x8 + 10)30 with initial guess 44.51, function (6x3 + 5x4 — 4x3 + 3x2 — 2x + 1)55 with initial - 2.0 and 33.41, function (ln[x2 + 3x + 5] — 2% + 7)31 for all initial guesses. Method 4 (M4) is best to use on function (e-%2 — e*2 — x8 + 10)30 with initial guess 1.3 and function (6x5 + 5x4 — 4x3 + 3x2 — 2x + 1)55 with initial guess 44.51. 2023 Thesis https://ir.uitm.edu.my/id/eprint/97760/ https://ir.uitm.edu.my/id/eprint/97760/1/97760.pdf text en public degree Universiti Teknologi MARA, Terengganu College of Computing, Informatics and Mathematics Salahudin, Nur Atikah
institution	Universiti Teknologi MARA
collection	UiTM Institutional Repository
language	English
advisor	Salahudin, Nur Atikah
topic	Analytical methods used in the solution of physical problems
spellingShingle	Analytical methods used in the solution of physical problems Khamsani, Nurlaila Azwa Application of air pollution data in Klang, Selangor to find multiple roots / Nurlaila Azwa Khamsani
description	Many types of methods such as Halley’s and super-Halley method, modified Newton’s method, and Schroder’s method can be used in finding multiple roots of nonlinear equations. Some methods cannot be used for finding multiple roots such as Newton’s method, Bisection method, Secant method, Muller’s method, and many more. Thus, the modifications of some methods did by few researchers. This project will find the month that has highest value of mean concentration of PM10 and PM2.5 with the value of concentrations. Next, this project will be implementing the highest mean concentrations of particulate matter which are PM10 and PM2.5 in Klang as the initial guesses for finding multiple roots. Lastly, every function with different initial guess has its own best method by identifying the smallest error and smallest CPU time. For Modified Newton’s method, it is best to use on function (e-x2 — ex2 — x8 + 10)30 with initial guess 33.41. For Method 1 (M1), it is best to use on function (e-x2 — ex2 — x8 + 10)30 with initial guess 44.51, function (6x3 + 5x4 — 4x3 + 3x2 — 2x + 1)55 with initial - 2.0 and 33.41, function (ln[x2 + 3x + 5] — 2% + 7)31 for all initial guesses. Method 4 (M4) is best to use on function (e-%2 — e*2 — x8 + 10)30 with initial guess 1.3 and function (6x5 + 5x4 — 4x3 + 3x2 — 2x + 1)55 with initial guess 44.51.
format	Thesis
qualification_level	Bachelor degree
author	Khamsani, Nurlaila Azwa
author_facet	Khamsani, Nurlaila Azwa
author_sort	Khamsani, Nurlaila Azwa
title	Application of air pollution data in Klang, Selangor to find multiple roots / Nurlaila Azwa Khamsani
title_short	Application of air pollution data in Klang, Selangor to find multiple roots / Nurlaila Azwa Khamsani
title_full	Application of air pollution data in Klang, Selangor to find multiple roots / Nurlaila Azwa Khamsani
title_fullStr	Application of air pollution data in Klang, Selangor to find multiple roots / Nurlaila Azwa Khamsani
title_full_unstemmed	Application of air pollution data in Klang, Selangor to find multiple roots / Nurlaila Azwa Khamsani
title_sort	application of air pollution data in klang, selangor to find multiple roots / nurlaila azwa khamsani
granting_institution	Universiti Teknologi MARA, Terengganu
granting_department	College of Computing, Informatics and Mathematics
publishDate	2023
url	https://ir.uitm.edu.my/id/eprint/97760/1/97760.pdf
_version_	1811768875536089088

Application of air pollution data in Klang, Selangor to find multiple roots / Nurlaila Azwa Khamsani

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