Solution and interpolation of one-dimensional heat equation by using cran-nicolson, Cubic Spline and Cubic B-Spline

Solution and interpolation of one-dimensional heat equation by using cran-nicolson, Cubic Spline and Cubic B-Spline

The purpose of this study is to apply the technique of Cubic Spline, Cubic BSpline and Crank-Nicolson in one-dimensional heat equations with Dirichlet boundary conditions. Then, their accuracy of numerical methods are compared by computing their absolute error and relative error. Those results of th...

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Main Author: Wan Sulaiman, Wan Khadijah
Format: Thesis
Language:English
Published: 2013
Subjects:
Q Science (General)
Online Access:http://eprints.utm.my/id/eprint/32522/1/WanKhadijahWanSulaimanMFS2013.pdf
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spelling my-utm-ep.325222017-09-18T07:24:45Z Solution and interpolation of one-dimensional heat equation by using cran-nicolson, Cubic Spline and Cubic B-Spline 2013-01 Wan Sulaiman, Wan Khadijah Q Science (General) The purpose of this study is to apply the technique of Cubic Spline, Cubic BSpline and Crank-Nicolson in one-dimensional heat equations with Dirichlet boundary conditions. Then, their accuracy of numerical methods are compared by computing their absolute error and relative error. Those results of the methods are calculated by using Matlab 2008 and Microsoft Visual Studio 2010 (C++). As the results, Crank- Nicolson is a good approximation solution since the result of relative error is quite close to the zero. Besides that, for interpolation method, cubic B-spline interpolation is found to give better results compare to the cubic spline interpolation since the relative error of cubic B-spline is better than cubic spline. Regarding to the findings, it can be seen clearly that the cubic spline, cubic B-spline and Crank-Nicolson are well approximated and give better results with smaller step size. 2013-01 Thesis http://eprints.utm.my/id/eprint/32522/ http://eprints.utm.my/id/eprint/32522/1/WanKhadijahWanSulaimanMFS2013.pdf application/pdf en public masters Universiti Teknologi Malaysia, Faculty of Science Faculty of Science
institution Universiti Teknologi Malaysia
collection UTM Institutional Repository
language English
topic Q Science (General)
spellingShingle Q Science (General)
Wan Sulaiman, Wan Khadijah
Solution and interpolation of one-dimensional heat equation by using cran-nicolson, Cubic Spline and Cubic B-Spline
description The purpose of this study is to apply the technique of Cubic Spline, Cubic BSpline and Crank-Nicolson in one-dimensional heat equations with Dirichlet boundary conditions. Then, their accuracy of numerical methods are compared by computing their absolute error and relative error. Those results of the methods are calculated by using Matlab 2008 and Microsoft Visual Studio 2010 (C++). As the results, Crank- Nicolson is a good approximation solution since the result of relative error is quite close to the zero. Besides that, for interpolation method, cubic B-spline interpolation is found to give better results compare to the cubic spline interpolation since the relative error of cubic B-spline is better than cubic spline. Regarding to the findings, it can be seen clearly that the cubic spline, cubic B-spline and Crank-Nicolson are well approximated and give better results with smaller step size.
format Thesis
qualification_level Master's degree
author Wan Sulaiman, Wan Khadijah
author_facet Wan Sulaiman, Wan Khadijah
author_sort Wan Sulaiman, Wan Khadijah
title Solution and interpolation of one-dimensional heat equation by using cran-nicolson, Cubic Spline and Cubic B-Spline
title_short Solution and interpolation of one-dimensional heat equation by using cran-nicolson, Cubic Spline and Cubic B-Spline
title_full Solution and interpolation of one-dimensional heat equation by using cran-nicolson, Cubic Spline and Cubic B-Spline
title_fullStr Solution and interpolation of one-dimensional heat equation by using cran-nicolson, Cubic Spline and Cubic B-Spline
title_full_unstemmed Solution and interpolation of one-dimensional heat equation by using cran-nicolson, Cubic Spline and Cubic B-Spline
title_sort solution and interpolation of one-dimensional heat equation by using cran-nicolson, cubic spline and cubic b-spline
granting_institution Universiti Teknologi Malaysia, Faculty of Science
granting_department Faculty of Science
publishDate 2013
url http://eprints.utm.my/id/eprint/32522/1/WanKhadijahWanSulaimanMFS2013.pdf
_version_ 1747816022592716800

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