الفهرس 
Chapter 1: Symmetry Analysis of Ordinary Differential EquationsOnly 14 pages are availabe for public view
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Abstract
In this work, Lie point symmetry method is utilized for solving ordinary differential equations (ODEs). This method is considered as an effective method for reducing the order of ODEs using change of variables. The aim of this thesis is to obtain some exact solutions of some engineering mathematical models using Lie point symmetry method. The thesis is organized in four chapters as follows: In chapter 1, Some basic definitions and theorems of symmetry method have been presented. Also the concepts of Lie group analysis and how to reduce the order of the ODEs have been introduced. In chapter 2, Some new bright and dark soliton solutions of ODEs arising from optical metamaterials models with parabolic law and polynomial law nonlinearities have been obtained. Lie symmetry method has enabled us to obtain these new solutions. In chapter 3, Two models of heat transfer have been presented, the first is the free boundary problem arising in n-diffusion equation and the second is the straight fin with temperature dependent thermal properties and internal heat generation. New exact solutions are obtained in each model using Lie symmetry method. In chapter 4, Conclusions and suggested future work have been given.