Solving burger’s equantion using explicit finite difference method and method of line

Burgers’ equation is a quasilinear differential equation can be solve either analytically or numerically. The analytical solutions use the Hopf-Cole transformation and reduced to diffusion equation. The focus of this research was to solve Burgers’ equation numerically by using Finite Difference Meth...

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Main Author:	Tan, Carrie Shiau Ying
Format:	Thesis
Language:	English
Published:	2017
Subjects:	QA Mathematics
Online Access:	http://eprints.utm.my/id/eprint/78538/1/CarrieTanShiauMFS2017.pdf
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spelling	my-utm-ep.785382018-08-27T03:22:19Z Solving burger’s equantion using explicit finite difference method and method of line 2017-06 Tan, Carrie Shiau Ying QA Mathematics Burgers’ equation is a quasilinear differential equation can be solve either analytically or numerically. The analytical solutions use the Hopf-Cole transformation and reduced to diffusion equation. The focus of this research was to solve Burgers’ equation numerically by using Finite Difference Method (FDM) and Method of Line (MOL) by using Fourth Order Runge-Kutta (RK4). The accuracy of MOL obtained solutions depends on the type of Ordinary Differential Equation (ODE) method used. The results obtained from both numerical method were compared between Hopf-Cole transformation analytical solutions. The simulations is coded by using MATLAB software. From the comparison, both methods shown to be good numerical approximation as the results obtained near to the exact solution. As the increase of spatial step size, the solutions obtained with be more accurate followed by individual methods’ restrictions. Different time and viscosity coefficient also tested to observe the changes of Burgers’ equation solutions. 2017-06 Thesis http://eprints.utm.my/id/eprint/78538/ http://eprints.utm.my/id/eprint/78538/1/CarrieTanShiauMFS2017.pdf application/pdf en public http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:108560 masters Universiti Teknologi Malaysia, Faculty of Science Faculty of Science
institution	Universiti Teknologi Malaysia
collection	UTM Institutional Repository
language	English
topic	QA Mathematics
spellingShingle	QA Mathematics Tan, Carrie Shiau Ying Solving burger’s equantion using explicit finite difference method and method of line
description	Burgers’ equation is a quasilinear differential equation can be solve either analytically or numerically. The analytical solutions use the Hopf-Cole transformation and reduced to diffusion equation. The focus of this research was to solve Burgers’ equation numerically by using Finite Difference Method (FDM) and Method of Line (MOL) by using Fourth Order Runge-Kutta (RK4). The accuracy of MOL obtained solutions depends on the type of Ordinary Differential Equation (ODE) method used. The results obtained from both numerical method were compared between Hopf-Cole transformation analytical solutions. The simulations is coded by using MATLAB software. From the comparison, both methods shown to be good numerical approximation as the results obtained near to the exact solution. As the increase of spatial step size, the solutions obtained with be more accurate followed by individual methods’ restrictions. Different time and viscosity coefficient also tested to observe the changes of Burgers’ equation solutions.
format	Thesis
qualification_level	Master's degree
author	Tan, Carrie Shiau Ying
author_facet	Tan, Carrie Shiau Ying
author_sort	Tan, Carrie Shiau Ying
title	Solving burger’s equantion using explicit finite difference method and method of line
title_short	Solving burger’s equantion using explicit finite difference method and method of line
title_full	Solving burger’s equantion using explicit finite difference method and method of line
title_fullStr	Solving burger’s equantion using explicit finite difference method and method of line
title_full_unstemmed	Solving burger’s equantion using explicit finite difference method and method of line
title_sort	solving burger’s equantion using explicit finite difference method and method of line
granting_institution	Universiti Teknologi Malaysia, Faculty of Science
granting_department	Faculty of Science
publishDate	2017
url	http://eprints.utm.my/id/eprint/78538/1/CarrieTanShiauMFS2017.pdf
_version_	1747818009783697408

Solving burger’s equantion using explicit finite difference method and method of line

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