Jominis, Rachel Aswin (2014) Numerical method for solving a nonlinear inverse diffusion equation. Masters thesis, Universiti Teknologi Malaysia, Faculty of Science.

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Abstract
Numerical Method is a way in solving a model of a problem mathematically and predicts the behaviour of the problem. That is why this method is very important for both natural and manmade process. Some basic theory of the Numerical Method has been applied in our daily life such as chemistry, physics, engineering, biology and others. The purpose of this project is to develop a numerical method for solving a onedimensional inverse problem. In order to solve the equation problem, some assumptions such as the existence and uniqueness of the inverse problem, are taken into consideration where auxiliary problem and Schauder Fixedpoint theorem were take place in order to prove it. Furthermore, a Numerical Algorithm such as Fully implicit Finitedifferent method and least square minimization method for solving a nonlinear inverse problem is proposed. At first, Taylor’s series Expansion is employed to linearize the nonlinear terms and then the finitedifferent method is used to discretize the problem. The present approach is to rearrange the system of linear differential equation into matrix form and then estimate the unknown diffusion coefficient via Leastsquare minimization method. Computer programming namely Maple 13 will be used as an additional method to improve the accuracy between the exact solution of the problem and the result from comparing the numerical method with a exact solution. Lastly, the graphing of the curve based from the result obtained will be done by using Maple 13. Throughout the project, we can conclude that all three objectives have been achieved.
Item Type:  Thesis (Masters) 

Additional Information:  Thesis (Sarjana Sains (Matematik))  Universiti Teknologi Malaysia, 2014 
Subjects:  Q Science > QA Mathematics 
Divisions:  Science 
ID Code:  48544 
Deposited By:  Haliza Zainal 
Deposited On:  15 Oct 2015 01:09 
Last Modified:  08 Aug 2017 07:15 
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