Solving ordinary differential equation by using Euler’s method and its variant based on MATLAB GUI / Muhammad Hanif Ghazali

Euler’s method is one of the most basic and simplest explicit methods to solve first- order ordinary differential equations (ODEs). The simplest approach for estimating initial value issues' solutions is Euler's method. The so-called "enhanced polygon method" or "modified Eu...

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Main Author:	Ghazali, Muhammad Hanif
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/97154/1/97154.pdf
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id	my-uitm-ir.97154
record_format	uketd_dc
spelling	my-uitm-ir.971542024-06-24T16:50:26Z Solving ordinary differential equation by using Euler’s method and its variant based on MATLAB GUI / Muhammad Hanif Ghazali 2023 Ghazali, Muhammad Hanif Analytical methods used in the solution of physical problems Euler’s method is one of the most basic and simplest explicit methods to solve first- order ordinary differential equations (ODEs). The simplest approach for estimating initial value issues' solutions is Euler's method. The so-called "enhanced polygon method" or "modified Euler technique," which enables a more accurate approximation of the answer, is another approach that is more helpful in numerical issues. Nowadays, it is vital and efficient to use numerical methods to obtain a rough solution to differential equations. The Euler strategy is the simplest, not just of all the methods, for estimating the solution to the initial value problem. The main objectives are to review the development of Euler’s method using bibliometric analysis and to develop a GUI for IVP ODE using Euler’s method and some of its variants. The study of solving ODE via Euler's method and its variant is applied to the process of building a GUI function in MATLAB. The literature review for the Euler's method and ODEs was produced in the second step using the bibliometric analysis. The results of solving ODEs using Euler's method and its variant based on GUI-MATLAB are then shown to determine which approach the most effective method based on the Mean Square Error and Computation time that generate from data of GUI-MATLAB on step size 0.1, 0.2, 0.5. The Runge-Kutta order 4 method, the Euler method, ODE23tb, and ODE23s had the lowest MSE and took the least amount of time to solve ODE problems. 2023 Thesis https://ir.uitm.edu.my/id/eprint/97154/ https://ir.uitm.edu.my/id/eprint/97154/1/97154.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	Analytical methods used in the solution of physical problems
spellingShingle	Analytical methods used in the solution of physical problems Ghazali, Muhammad Hanif Solving ordinary differential equation by using Euler’s method and its variant based on MATLAB GUI / Muhammad Hanif Ghazali
description	Euler’s method is one of the most basic and simplest explicit methods to solve first- order ordinary differential equations (ODEs). The simplest approach for estimating initial value issues' solutions is Euler's method. The so-called "enhanced polygon method" or "modified Euler technique," which enables a more accurate approximation of the answer, is another approach that is more helpful in numerical issues. Nowadays, it is vital and efficient to use numerical methods to obtain a rough solution to differential equations. The Euler strategy is the simplest, not just of all the methods, for estimating the solution to the initial value problem. The main objectives are to review the development of Euler’s method using bibliometric analysis and to develop a GUI for IVP ODE using Euler’s method and some of its variants. The study of solving ODE via Euler's method and its variant is applied to the process of building a GUI function in MATLAB. The literature review for the Euler's method and ODEs was produced in the second step using the bibliometric analysis. The results of solving ODEs using Euler's method and its variant based on GUI-MATLAB are then shown to determine which approach the most effective method based on the Mean Square Error and Computation time that generate from data of GUI-MATLAB on step size 0.1, 0.2, 0.5. The Runge-Kutta order 4 method, the Euler method, ODE23tb, and ODE23s had the lowest MSE and took the least amount of time to solve ODE problems.
format	Thesis
qualification_level	Bachelor degree
author	Ghazali, Muhammad Hanif
author_facet	Ghazali, Muhammad Hanif
author_sort	Ghazali, Muhammad Hanif
title	Solving ordinary differential equation by using Euler’s method and its variant based on MATLAB GUI / Muhammad Hanif Ghazali
title_short	Solving ordinary differential equation by using Euler’s method and its variant based on MATLAB GUI / Muhammad Hanif Ghazali
title_full	Solving ordinary differential equation by using Euler’s method and its variant based on MATLAB GUI / Muhammad Hanif Ghazali
title_fullStr	Solving ordinary differential equation by using Euler’s method and its variant based on MATLAB GUI / Muhammad Hanif Ghazali
title_full_unstemmed	Solving ordinary differential equation by using Euler’s method and its variant based on MATLAB GUI / Muhammad Hanif Ghazali
title_sort	solving ordinary differential equation by using euler’s method and its variant based on matlab gui / muhammad hanif ghazali
granting_institution	Universiti Teknologi MARA, Terengganu
granting_department	College of Computing, Informatics and Mathematics
publishDate	2023
url	https://ir.uitm.edu.my/id/eprint/97154/1/97154.pdf
_version_	1804890015269912576

Solving ordinary differential equation by using Euler’s method and its variant based on MATLAB GUI / Muhammad Hanif Ghazali

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