Weight Monte Carlo algorithms for estimation and parametric analysis of the solution to the kinetic coagulation equation

The Smoluchowski equation with linear coagulation coefficients depending on two parameters is considered. We construct weight algorithms for estimating various linear functionals in an ensemble that is governed by the equation under study. The algorithms constructed allow us to estimate the functionals for various parameters, as well as parametric derivatives by using the same set of trajectories. Moreover, we construct the value algorithms and analyze their efficiency for estimating the total monomer concentration, as well as the total monomer and dimer concentration in the ensemble. The computational cost is considerably reduced via the approximate value simulation of the time between interactions combined with the value simulation of the interacting pair number.