Maser transitions are commonly observed in media exhibiting a large range of
densities and temperatures. They can be used to obtain information on the
dynamics and physical conditions of the observed regions. In order to obtain
reliable constraints on the physical conditions prevailing in the masing
regions, it is necessary to model the excitation mechanisms of the energy
levels of the observed molecules. We present a numerical method that enables us
to obtain self-consistent solutions for both the statistical equilibrium and
radiative transfer equations. Using the standard maser theory, the method of
Short Characteristics is extended to obtain the solution of the
integro-differential radiative transfer equation, appropriate to the case of
intense masing lines. We have applied our method to the maser lines of the H2O
molecule and we compare with the results obtained with a less accurate
approach. In the regime of large maser opacities we find large differences in
the intensity of the maser lines that could be as high as several orders of
magnitude. The comparison between the two methods shows, however, that the
effect on the thermal lines is modest. Finally, the effect introduced by rate
coefficients on the prediction of H2O masing lines and opacities is discussed,
making use of various sets of rate coefficients involving He, o-H2 and p-H2. We
find that the masing nature of a line is not affected by the selected
collisional rates. However, from one set to the other the modelled line
opacities and intensities can vary by up to a factor ~2 and ~10 respectively
