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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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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
score 13.214268

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