In this paper numerical schemes are discussed to reduce the computational work involved with the evaluation of the aerodynamic influence coefficients of panel methods. The applicability of these schemes is investigated to the calculation of potential flow around an airfoil. The interest concerns the decomposition of the boundary integral operator by splitting the contour integration such that the singular behaviour of the kernelfunction near the trailing edge is taken into account. The decomposition results in a compact operator and a contractive operator. The compact operator contains a smooth kerneIfunction, which is approximated by piecewise linear interpolation. The interpolation provides error terms of the same order as the panel method. For a fixed number of panels the accuracy, however, has been decreased significantly. Paper presented at the 3rd GAMM-Seminar Kiel on Panel Methods in Mechanics, Kiel, January 16-18, 1987.