Numerical simulation of the burger's equation

Master of Science in Engineering Mathematics

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Bibliographic Details
Main Author:	Intan Mastura, Ramlee
Other Authors:	Nursalasawati, Rusli, Dr.
Format:	Dissertation
Language:	English
Published:	Universiti Malaysia Perlis (UniMAP) 2016
Subjects:	Differential equations, Partial Finite differences Burgers’ equation Solution
Online Access:	http://dspace.unimap.edu.my:80/xmlui/handle/123456789/77065
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Institution:	Universiti Malaysia Perlis
Language:	English

id	my.unimap-77065
record_format	dspace
spelling	my.unimap-770652022-11-17T04:46:05Z Numerical simulation of the burger's equation Intan Mastura, Ramlee Nursalasawati, Rusli, Dr. Differential equations, Partial Finite differences Burgers’ equation Solution Master of Science in Engineering Mathematics In this study, the exponential finite difference technique has been used to solve one-dimensional Burgers’ equation with different value of h (step size). Burgers’ equation is considered in this study because the equation governing simple nonlinear diffusion process. Since Burgers’ equation is nonlinear equation, the Hopf-Cole transformation has been applied to convert the equation to one-dimensional heat equation. Consequently, the exponential finite difference method has been used to generate of one-dimensional heat equation. Three techniques called explicit exponential finite difference method, implicit exponential finite difference method and modified Burgers’ equation using explicit exponential finite difference method have been implemented. In the solution process, the explicit exponential finite difference method used a direct to solve the Burgers’ equation while the implicit exponential finite difference method leads to a system of nonlinear equation. At each time-level, Newton’s method is used to solve the nonlinear system. The solution of the onedimensional modified Burgers’ equation by using the explicit exponential finite difference method. The solution process have been discretized the time derivative and spatial derivative using exponential finite difference technique. Numerical solutions for each method are compared with exact solution and the results obtained using three methods are precise and reliable. The percent errors are compute and found to be sufficiently small. 2016 2022-11-17T04:44:12Z 2022-11-17T04:44:12Z Dissertation http://dspace.unimap.edu.my:80/xmlui/handle/123456789/77065 en Universiti Malaysia Perlis (UniMAP) Universiti Malaysia Perlis (UniMAP) Institute of Engineering Mathematics
institution	Universiti Malaysia Perlis
building	UniMAP Library
collection	Institutional Repository
continent	Asia
country	Malaysia
content_provider	Universiti Malaysia Perlis
content_source	UniMAP Library Digital Repository
url_provider	http://dspace.unimap.edu.my/
language	English
topic	Differential equations, Partial Finite differences Burgers’ equation Solution
spellingShingle	Differential equations, Partial Finite differences Burgers’ equation Solution Intan Mastura, Ramlee Numerical simulation of the burger's equation
description	Master of Science in Engineering Mathematics
author2	Nursalasawati, Rusli, Dr.
author_facet	Nursalasawati, Rusli, Dr. Intan Mastura, Ramlee
format	Dissertation
author	Intan Mastura, Ramlee
author_sort	Intan Mastura, Ramlee
title	Numerical simulation of the burger's equation
title_short	Numerical simulation of the burger's equation
title_full	Numerical simulation of the burger's equation
title_fullStr	Numerical simulation of the burger's equation
title_full_unstemmed	Numerical simulation of the burger's equation
title_sort	numerical simulation of the burger's equation
publisher	Universiti Malaysia Perlis (UniMAP)
publishDate	2016
url	http://dspace.unimap.edu.my:80/xmlui/handle/123456789/77065
_version_	1751537839050326016

Numerical simulation of the burger's equation

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