On the numerical solution of the direct scattering problem for an open sound-hard arc

We derive a hypersingular integral equation, which is equivalent to the scattering problem. Using the cosine substitution, we obtain an integral equation which is closely related to the integral equation for the case of a closed boundary. We solve this equation approximately by a quadrature formula method and obtain pointwise error estimates in Hِlder norms by using a perturbation argument.