الفهرس 
INTRODUCTION ON DIFFERENTIAL EQUATIONSOnly 14 pages are availabe for public view
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Abstract
Many problems in engineering and science fields can be described by the differential equations; therefore solving differential equations (DEs) is a very necessity in the context of Applied Mathematics, Theoretical Physics and Engineering Sciences. Many of analytical and numerical methods have been developed to obtain accurate approximate and analytic solutions for the problems in the literature. The investigation of the approximate or exact solution helps to understand the means of these problems. Recently, some researchers used many powerful methods for obtaining approximate or exact solutions of nonlinear differential equations, such as homotopy perturbation method (HPM), variational iteration method (VIM), modified variational iteration method (MVIM), Adomian Decomposition Method (ADM), and Differential Transform Method (DTM).
This thesis entitled ”Analytical and Numerical treatment for Initial- Boundary Value problems” discusses some analytical solutions to some of the nonlinear differential equations, using Differential Transform Method and other methods.
The thesis has been divided into four chapters.
Chapter one is intended to introduce the general classification of differential equations and basic concepts are discussed. A summary of the literature available on the subject and summary of the work presented in the thesis also is showed in this chapter.
In the second chapter, is reviewed some of the most important of these methods, for example, ADM, HPM, VIM, LVIM.
In the third chapter, the methodology of the differential transforms method has been presented. An unsteady axisymmetric squeezing fluid flow with slip and no-slip boundaries and an unsteady axisymmetric flow of no conducting, Newtonian fluid squeezed flow between two circular
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plates passing through the porous media channel with slip and no-slip boundary conditions have been solved by using the Differential Transform. We have obtained analytical solutions and compare them by using classical methods.
In the fourth chapter, were given discussion and conclusions.
It is worth to mention that:
All calculations were done by using of ”Mathematica 10”