The Numerical Solution of Singular Integral Equations over $( - 1,1)$

An algorithm is described for the approximate solution of a complete singular integral equation (with Cauchy principal value integral) taken over the arc $( - 1,1)$. The coefficients in the dominant part of this equation are not necessarily restricted to be constants so that the approximate solution of a wide class of singular integral equations is possible. No restriction is placed on the index of the equation.