الفهرس 
IntroductionOnly 14 pages are availabe for public view
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Abstract
Group method is considered one of the important analytical methods for overcoming the difficulties, which arise in solving nonlinear partial differential equations. This’thesis is focused on the application of group method for solving boundary-value problems. The present procedure is Abd-el-Malek and his Co-workers procedure.
Application of s-parameter transformation group reduces the system of governing partial differential equation(s) with the auxiliary conditions to a system of ordinary differential equation(s) with the appropriate corresponding conditions. The reduced system can be solved analytically or numerically.
The thesis is made up of six chapters, which are:
Chapter (1)
It is an introductory chapter concerning partial differential equations. We derive the equations governing some physical phenomena such as Wave equation and Heat equation. We introduce Laplace equation and Poisson equation and show how the additional factors can be taken into consideration to transform the linear partial differential equations into ordinary differential equations.
Also, different types of the nonlinear diffusion equations and some generalized Burgers’equations are given. Finally, some of the published papers related to these equations, together with the corresponding physical phenomena are also introduced.
Chapter (2)
In this chapter, we introduce some transformations, which are used in solving nonlinear partial differential equations. Also, we resume the history of the group methods. Giving the main steps for applying this method to transform partial differential equations into ordinary differential equations concludes this chapter.
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Chapter (3)
The group method is used to solve Multi-dimensional diffusion equation.
Effect of different parameters, which appear in this equation and the time on the concentration diffusion function, has been studied.
Chapter (4)
Following the same procedure of chapter 3, the fission product behavior in nuclear fuel is found by solving a nonlinear diffusion equation. We obtained numerical solution for the concentration of gas atoms using nonlinear finite difference method. Also, we studied the effect of time on this concentration.
Chapter (5)
Following the same procedure of the pervious chapters, we solved Rayleigh problem for a power law non-Newtonian conducting fluid. We obtained numerical solution for the velocity of the fluid and we studied the effect of all parameters, which appear in the problem and the time on the velocity of the fluid.
Chapter (6)
The conclusions and the future work are given.