Regarding the design problem of corrugated planar optical waveguide filters, a new numerical method is presented consisting of a direct numerical solution of the coupled Gel'fand-Levitan-Marchenko integral equations. This method, which uses leapfrogging in space and time, is exact in principle and avoids some difficulties encountered in previously derived analytical methods of solution. Straightforward numerical calculations permit the design of several classes of filters such as Butterworth, Chebyshev, Cauer (elliptic) and others, as presented in the paper. The accuracy of our proposed method of design is checked in several ways, mainly through the numerical solution of the corresponding direct-scattering problem (Riccati differential equation).