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Numerical solution for a class of singular integral equations

This paper is concerned with finding approximate solution for the singular integral equations. Relating the singular integrals to Cauchy principal-value integrals, we expand the kernel and the density function of singular integral equation by the sum of the chebyshev polynomials of the first, second, third and fourth kinds. Some numerical examples are presented to illustrate the accuracy and effectiveness of the present work. Numerical results show that the errors of approximate solutions of examples in different cases with small value of  are very small. These show that the methods developed are very accurate and in fact for a linear function give the exact solution. 
 
 Key words: Singular integral equations, Cauchy kernel, chebyshev polynomials, weight functions.