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 ordinary or partial differential equations. This thesis is focused on the application of Lie-group method to the dynamical systems, especially fluid dynamics problems. Application of Lie-group method reduces the system of governing partial differential equations with the auxiliary conditions to a system of ordinary differential equations with the appropriate corresponding conditions. The reduced system can be solved analytically or numerically. The thesis is made up of five chapters, which are: Chapter (1) It is an introductory chapter concerning MHD systems. We define the meaning of MHD and introduce a brief history of MHD. Also, Types of MHD, its equations and their derivations. Chapter (2- This chapter is concerned with the most important equations governing the fluid dynamics, which are Navier-Stokes equations. In three-dimensional case, derivation of these equations and also the continuity equation are made in Cartesian form. Also, the Navier-Stokes equations are written in other coordinates (cylindrical and spherical) without proof. Chapter (3) In this chapter, we resume the history of the group methods. We introduce the concept of applying Lie-group method to both first and higher order ordinary differential equations, also to systems of ordinary differential equations. Then, we extended our work to show how this method is applied to partial differential equations. Chapter (4) In this chapter, we apply Lie-group method to get the solution of the problem ”Lie-group method of solution for MHD viscous flow over stretching sheet”. The resulting system of nonlinear differential equations is then solved numerically using shooting method coupled with Runge-Kutta scheme. Chapter (5)The conclusions and the future work are given.