الفهرس 
Introduction and survey on basic methods of solutions of csieOnly 14 pages are availabe for public view
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Abstract
Most of the known direct methods for solving Cauchy Singular Integral Equations (CSIEs) convert the problem to the solution of a system of linear algebraic equations. Such methods are not appropriate in the cases for which the number of equations in the system is very large because of computer memory and CPU time limitations. Iterative methods, on the other hand, require less memory and fewer computation steps. In this thesis, we present three proposed iterative methods to solve CSIE. In the first method, the second iterative method of Atkinson to solve CSIE is used; the rate of convergence is considered and numerical examples are given to demonstrate the practical usefulness of the presented algorithm. In the second method, the use of a threelevel iterative technique for solving CSIE of the first kind is proposed. We present a general form of a family of iterative methods, which contains the first and the second proposed iterative methods as special cases. In the third method, a modification of the second iterative method of Atkinson used to solve CSIE is established. This modification is shown to give faster rate of convergence than the second iterative method of Atkinson. ?The present thesis is organized in six chapters as follows: Chapter (1) contains a general introduction and a survey on direct and indirect quadrature solutions of CSIEs. Chapter (2) presents an algorithm for solving a system of CSIEs. Chapter (3) deals with two grid iterative techniques for solving CSIEs. In chapter (4), multiple grid methods for the solution of CSIEs of the first kind is introduced. In chapter (5), we present a modified iterative algorithm for the numerical solution of CSIE. Finally, in chapter (6), a conclusion is given and topics for the future work are suggested.