Abstract
Several problems of mathematical physics are reducible to singular integral equations of the first kind with Cauchy-type kernels. In this paper an iterative method for the numerical solution of this class of equations is proposed. This method can be considered analogous to the existing iterative methods for the numerical solution of Fredholm integral equations of the second kind and is based on the Gauss- and Lobatto-Chebyshev quadrature rules. The method is applied to some plane elasticity crack problems and is seen to give convergent results. The application of the proposed method to other singular integral equations appearing in physical and engineering problems, either without modifications or after appropriate modifications, is trivial.
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