We study the problem of the scattering of the first TM guided mode from an abruptly ended strongly asymmetrical slab waveguide by an improved iteration technique, which is based on the integral equation method with "accelerating" parameters. We demonstrate that the values of these parameters are related to the variational principle, and we save approximately 1-2 iterations compared with the case in which these parameters are not employed. The tangential electric-field distribution on the terminal plane, the reflection coefficient of the first TM guided mode, and the far-field radiation pattern are computed. Furthermore, a simple technique based on the Aitken extrapolation procedure is employed for faster computation of the higher-order solutions of the reflection coefficient. Numerical results are presented for several cases of abruptly ended waveguides, including systems with variational profile, while special attention is given to the far-field radiation pattern rotation and its explanation.