Universiti Teknologi Malaysia Institutional Repository

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

Wan Sulaiman, Wan Khadijah (2013) Solution and interpolation of one-dimensional heat equation by using cran-nicolson, Cubic Spline and Cubic B-Spline. Masters thesis, Universiti Teknologi Malaysia, Faculty of Science.

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Abstract

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.

Item Type:Thesis (Masters)
Additional Information:Thesis (Sarjana Sains (Matematik)) - Universiti Teknologi Malaysia, 2013; Supervisor : Hamisan Rahmat
Uncontrolled Keywords:heat equation, splines, interactive computer systems
Subjects:Q Science > Q Science (General)
Divisions:Science
ID Code:32522
Deposited By: Kamariah Mohamed Jong
Deposited On:30 Oct 2013 11:05
Last Modified:18 Sep 2017 15:24

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