Group method for solving boundary-value problems

In most physical and engmeenng applications, the investigatedphenomena are formulated in a mathematical form as the linear andnonlinear partial differential equations. The well-known standard methodsof solution may yield exact solutions to a number of problems especiallywhen they are linear. Nonlinear problems have always tantalized scientistsand engineers: they fascinate, but oftentimes elude exact treatment.Group methods are considered as a class of the important analyticalmethods for solving the linear and nonlinear partial differential equations.The thesis is concerned with the application of the group method forsolving boundary-value problems. Problems including a single equation ora system of partial differential equations are considered in the thesis. Theprocedure applied here is that of Abd-el-Malek and his eo-workers.The application of the present procedure reduces systematically thegoverning partial differential equation(s) with the auxiliary conditions toordinary one(s) with the corresponding conditions. The reduced equation(s)with the related conditions can then be solved analytically, if possible, ornumerically to introduce the solution of the original equation(s).The thesis is made up of six chapters which are:Chapter (1)It is an introductory chapter concerning nonlinear partial differentialequations. Noniinear diffusion equations are-presented including different’,forms which frequently arise in physics. Boundary-layer equations; thedefinitions, related parameters and derivation of equations are introduced.Equations of boundary-layer flow of power-law fluids are aiso given. For