Piecewise constant Galerkin method for a class of Cauchy singular integral equations of the second kind in L2

In this work, we present piecewise constant Galerkin method for a class of Cauchy singular integral equations of the second kind with constant coefficients in L2([0,1],C), using a sequence of orthogonal finite rank projections. We prove the existence and uniqueness theorems for the Cauchy integral equation and the approximate equation, respectively. We perform the error analysis for which we give new and improved estimates for the rates of convergence. Numerical example illustrates the theoretical results.