  We present an efficient numerical code based on spectral methods to integrate
the field equations of general Robinson-Trautmann spacetimes. The most natural
basis functions for the spectral expansion of the metric functions are
spherical harmonics. Using the values of appropriate combinations of the metric
functions at the collocation points, we have managed to reduce expression swell
when the number of spherical harmonics increases. Our numerical code runs with
relatively little computational resources and the code tests have shown
excellent accuracy and convergence. The code has been applied to situations of
physical interest in the context of Robsinson-Trautmann geometries such as:
perturbation of the exterior gravitational field of a spheroid of matter;
perturbation of an initially boosted black hole; and the non-frontal collision
of two Schwarzschild black holes. In dealing with these processes we have
derived analytical lower and upper bounds on the velocity of the resulting
black hole and the efficiency of the gravitational wave extraction,
respectively. Numerical experiments were performed to determine the forms of
the gravitational waves and the efficiency in each situation of interest.
