A FREDHOLM INTEGRAL-EQUATION OF THE 2ND KIND FOR CONFORMAL MAPPING

We present a Fredholm integral equation of the second kind for the derivative of the boundary correspondence function theta of the conformal mapping of a Jordan region with piecewise twice differentiable boundary onto the unit disk. One of our derivations of the equation leads to a more general regularization procedure for some singular integral equations of the first kind. The integral equation can be solved numerically by applying the Fourier method; the convergence to theta prime in L//2 of the solution of the discrete equation so obtained follows by simple theorems. Examples show that the equation often yields better numerical results than both a related method proposed by Henrici and Warschawski's equation.