Solving nonlinear system of equations based on MATLAB GUI / Muhammad Azri Azman Shah

Nonlinear systems are prevalent in numerous scientific and engineering fields, presenting unique challenges due to their complex behavior and the potential for multiple solutions. The numerical methods implemented in this project include Newton's Method, Broyden's Method, the Broyden-Fletc...

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Main Author:	Azman Shah, Muhammad Azri
Format:	Thesis
Language:	English
Published:	2024
Subjects:	Evolutionary programming (Computer science) Genetic algorithms
Online Access:	https://ir.uitm.edu.my/id/eprint/105929/1/105929.pdf
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id	my-uitm-ir.105929
record_format	uketd_dc
spelling	my-uitm-ir.1059292024-11-30T23:08:43Z Solving nonlinear system of equations based on MATLAB GUI / Muhammad Azri Azman Shah 2024 Azman Shah, Muhammad Azri Evolutionary programming (Computer science). Genetic algorithms Nonlinear systems are prevalent in numerous scientific and engineering fields, presenting unique challenges due to their complex behavior and the potential for multiple solutions. The numerical methods implemented in this project include Newton's Method, Broyden's Method, the Broyden-Fletcher-Goldfarb-Shanno (BFGS) Method, the Steepest Descent (SD), and Fsolve method. The main objectives of this project were to review the results of applying the Newton, Broyden, BFGS, SD, and Fsolve methods to the numerical solution of a system of nonlinear equations and to create a user-friendly MATLAB GUI that simplifies the process for users. The solver accepts user inputs for functions, jacobians, and initial values, and outputs the number of iterations, norm of gradients to reach a solution. Extensive testing was conducted using ten standard test functions to evaluate the performance of each method. The results demonstrate that while Newton's Method generally converges faster, Broyden's and BFGS Methods offer computational advantages in scenarios where the Jacobian matrix is challenging to compute. The SD Method, although slower, provides reliable convergence for specific types of problems. This project not only highlights the strengths and weaknesses of each numerical method but also contributes a practical tool for researchers and engineers to solve complex nonlinear systems efficiently. The developed MATLAB GUI stands out for its ease of use, visual appeal, and adaptability to various applications, making it a valuable addition to the computational tools available in mathematical modelling and analytics. 2024 Thesis https://ir.uitm.edu.my/id/eprint/105929/ https://ir.uitm.edu.my/id/eprint/105929/1/105929.pdf text en public degree Universiti Teknologi MARA, Terengganu College of Computing, Informatics and Mathematics Norddin, Nur Idalisa
institution	Universiti Teknologi MARA
collection	UiTM Institutional Repository
language	English
advisor	Norddin, Nur Idalisa
topic	Evolutionary programming (Computer science) Genetic algorithms
spellingShingle	Evolutionary programming (Computer science) Genetic algorithms Azman Shah, Muhammad Azri Solving nonlinear system of equations based on MATLAB GUI / Muhammad Azri Azman Shah
description	Nonlinear systems are prevalent in numerous scientific and engineering fields, presenting unique challenges due to their complex behavior and the potential for multiple solutions. The numerical methods implemented in this project include Newton's Method, Broyden's Method, the Broyden-Fletcher-Goldfarb-Shanno (BFGS) Method, the Steepest Descent (SD), and Fsolve method. The main objectives of this project were to review the results of applying the Newton, Broyden, BFGS, SD, and Fsolve methods to the numerical solution of a system of nonlinear equations and to create a user-friendly MATLAB GUI that simplifies the process for users. The solver accepts user inputs for functions, jacobians, and initial values, and outputs the number of iterations, norm of gradients to reach a solution. Extensive testing was conducted using ten standard test functions to evaluate the performance of each method. The results demonstrate that while Newton's Method generally converges faster, Broyden's and BFGS Methods offer computational advantages in scenarios where the Jacobian matrix is challenging to compute. The SD Method, although slower, provides reliable convergence for specific types of problems. This project not only highlights the strengths and weaknesses of each numerical method but also contributes a practical tool for researchers and engineers to solve complex nonlinear systems efficiently. The developed MATLAB GUI stands out for its ease of use, visual appeal, and adaptability to various applications, making it a valuable addition to the computational tools available in mathematical modelling and analytics.
format	Thesis
qualification_level	Bachelor degree
author	Azman Shah, Muhammad Azri
author_facet	Azman Shah, Muhammad Azri
author_sort	Azman Shah, Muhammad Azri
title	Solving nonlinear system of equations based on MATLAB GUI / Muhammad Azri Azman Shah
title_short	Solving nonlinear system of equations based on MATLAB GUI / Muhammad Azri Azman Shah
title_full	Solving nonlinear system of equations based on MATLAB GUI / Muhammad Azri Azman Shah
title_fullStr	Solving nonlinear system of equations based on MATLAB GUI / Muhammad Azri Azman Shah
title_full_unstemmed	Solving nonlinear system of equations based on MATLAB GUI / Muhammad Azri Azman Shah
title_sort	solving nonlinear system of equations based on matlab gui / muhammad azri azman shah
granting_institution	Universiti Teknologi MARA, Terengganu
granting_department	College of Computing, Informatics and Mathematics
publishDate	2024
url	https://ir.uitm.edu.my/id/eprint/105929/1/105929.pdf
_version_	1818588162394423296

Solving nonlinear system of equations based on MATLAB GUI / Muhammad Azri Azman Shah

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