Anderson acceleration method of finding steady-state particle size distribution for a wide class of aggregation-fragmentation models

A fast numerical method of finding steady-state distributions of particles sizes for a wide class of aggregation-fragmentation models, including the models with a source of monomers is developed. The method is based on a fast evaluation scheme for large sets of non-linear Smoluchowski-type ODE with an application of the Anderson acceleration method of the fixed point iterations. In the numerical tests of the suggested approach we demonstrate that huge sets of non-linear ODE may be solved with high precision in terms of Euclidian norm of the residual in modest times with use of a regular desktop computer. We compare our numerical solutions with the known analytical results for the steady-state distributions as well as with the other fast numerical schemes and prove the high accuracy of the novel method and its significant superiority with respect to the existing fast numerical method of solution of the addressed problems.