A new modification of the integral equation method using an iteration technique with "accelerating" parameters is presented to solve the problem of guided-mode scattering from an abruptly ended asymmetrical slab waveguide. The optimal choice of the parameters is shown to be closely connected with the variational principle. The electric-field distribution at the terminal plane, the reflection coefficient of the guided mode, and the far-field radiation pattern are computed. Numerical results are presented for several cases of abruptly ended waveguides, including the systems with constant and variable profiles of the refractive indices. The phenomenon of the radiation pattern rotation is examined in detail.