Evolution of raindrop spectra. Part I: solution to the stochastic collection/breakup equation using the method of moments

We prove that the collisional breakup equation conserves overall mass irrespective of the degree to which the fragment distribution function conserves mass for individual collisions. The proposed method produces better approximations to the analytical solutions for simple kernels, than those obtained using a single moment method. In writing the breakup terms, an approximation to the breakup kernel and fragment distribution function in discrete categories is used. This approach allows one to write the algorithm without prescribing the shape of the distribution function within the category. -from Authors