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An effective numerical method for analyzing edge-type scattering problems is presented with its analytical foundations. The general theory is applied to an arbitrarily shaped two-dimensional scatterer with an edge point, convergence of the approximate solutions is proven, and an algorithm for numerical computation is derived. The algorithm is employed for the resolution of the problem of a rectangular cylinder. Numerical data on the speed of the convergence show the validity and the efficiency of this method. Some examples for far-field patterns and back scattering cross sections as functions of the wavenumber are given.