Numerical Solution of Singular Integral Equations: Methods
by Pericles S. Theocaris, (Prof., Chair of Mech. A’, Athens National Technical Univ., 5 K. Zographou St., Zographou, Athens 624, Greece)
Journal of the Engineering Mechanics Division, Vol. 107, No. 5, September/October 1981, pp. 733752, (doi: http://dx.doi.org/10.1061/JMCEA3.0002002)
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Journal Paper 
Abstract: 
Several methods for the numerical solution of Cauchytype singular integral equations, frequently encountered in twodimensional elasticity, are established. The well known numerical integration rules are properly combined in order to handle numerically Cauchytype singular integral equations along the integration interval [1, 1] and for a large variety of weight functions. In this way, such an equation (or a system of such equations) can be numerically sloved by reduction to a system of linear equations. For this reduction, the singular integral equation is applied to a number of appropriately selected points of the integration interval, and then a numerical integration rule is used for the approximation of the integrals in this equation. 
