Energy absorption is assumed to take place through the generation of large amplitude plasma waves propagating outwards from the critical surface, and the effect of these waves on the particle distribution is described by a quasi-linear equation with non-linear broadening of the resonance. Instead of solving for the wave amplitude and particle distribution function simultaneously, a form for the wave amplitude is chosen from physical considerations, with a damping coefficient chosen to give conservation of energy. With this simplification results are obtained over a range of parameters, without a great deal of computational effort.