الفهرس 
IntroductionOnly 14 pages are availabe for public view
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Abstract
Throughout this thesis we have been described a Green’s function for the 2-D Helmholtz equation in finite and infinite domains. For the finite domain under consideration, the rectangle in Cartesian coordinates, Green’s function and spectral added method are described for solving Helmholtz equation subject to Dirichlet boundary conditions. For an infinite domain, infinite strip, Green’s function is usually expressed as a series of images which is slowly convergent, and that is why we transform it into a more convenient representation, which is rapidly convergent and stable.
We have centered ourselves throughout chapter 3 with the solution of Navier-stokes (N-S) equations. Our discussion consists of two main parts, the first one is the solution of two dimensional N-S equations in vorticity-stream function formulation ( - ) by means of Green’s function. This technique is used for solving the coupling between vorticity and stream function at the boundary of the domain. The second part of chapter two is the solution of N-S equations in vorticity-velocity formulation ( -V) by using Green’s function and influence matrix method.
In the last chapter, we use a more convenient technique to generate a faster convergent Green’s function needed for solving three-dimensional Laplace’s equation in two cases: the first domain is bounded by two parallel planes; and the second is an infinite open rectangular channel. For each case, we discus and deduce its different forms of Green’s functions which are rapidly convergent. Also, at the end of this chapter, many examples are given and discussed for the numerical applications of the above two cases; and then we make a comparison between our calculations and some others.