Approximate solution of dual integral equations

We study dual integral equations which appear in formulation of theý ýpotential distribution of an electrified plate with mixed boundaryý ýconditionsý. ýThese equations will be converted to a system ofý ýsingular integral equations with Cauchy type kernelsý. ýUsingý ýChebyshev polynomialsý, ýwe propose a method to approximate theý ýsolution of Cauchy type singular integral equation which will beý ýused to approximate the solution of the main dual integralý ýequationsý. ýNumerical results demonstrate effectiveness of this method.