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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
https://ir.uitm.edu.my/id/eprint/97154/
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spelling my.uitm.ir.971542024-06-24T16:50:26Z https://ir.uitm.edu.my/id/eprint/97154/ Solving ordinary differential equation by using Euler’s method and its variant based on MATLAB GUI / Muhammad Hanif Ghazali 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 NonPeerReviewed text en https://ir.uitm.edu.my/id/eprint/97154/1/97154.pdf Solving ordinary differential equation by using Euler’s method and its variant based on MATLAB GUI / Muhammad Hanif Ghazali. (2023) 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
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
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
publishDate 2023
url https://ir.uitm.edu.my/id/eprint/97154/1/97154.pdf
https://ir.uitm.edu.my/id/eprint/97154/
_version_ 1802981114884653056
score 13.211869

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