Approximate solution of dual integral equations

We study dual integral equations which appear in formulation of the potential distribution of an electri ed plate with mixed boundary conditions. These equations will be converted to a system of singular integral equations with Cauchy type kernels. Using Chebyshev polynomials, we propose a method to approximate the solution of Cauchy type singular integral equation which will be used to approximate the solution of the main dual integral equations. Numerical results demonstrate effectiveness of this method.