[en] A practical numerical method for the effective solution of the Thomson Problem is proposed. The developed iterative algorithm allows to conduct theoretical researches such as study of the number of asymptotic solutions depending on the particle count. Metastable states of charged point systems on a unit sphere were considered and the probability of falling into the basin of each state was obtained. Founded upon the algorithm and dual lattice representation approach, the framework for rapid construction of capped carbon nanotubes was created. (paper)