Weighted Monte Carlo method for an approximate solution of the nonlinear coagulation equation

New weighted modifications of direct statistical simulation methods designed for the approximate solution of the nonlinear Smoluchowski equation are developed on the basis of stratification of the interaction distribution in a multiparticle system according to the index of a pair of interacting particles. The weighted algorithms are validated for a model problem with a known solution. It is shown that they effectively estimate variations in the functionals with varying parameters, in particular, with the initial number $N_0$ of particles in the simulating ensemble. The computations performed for the problem with a known solution confirm the semiheuristic hypothesis that the model error is $O(N_0^{-1})$. Estimates are derived for the derivatives of the approximate solution with respect to the coagulation coefficient.