Investigation of numerical methods for solving the Vlasov equation by its exact solutions

Numerical methods for solving the Vlasov equation for a charged particle beam based on the method of macroparticles are considered. For solving of the boundary problem for the self field of a beam, an adaptive grid method is applied. This method gives a possibility to increase accuracy of computations. To estimate the accuracy of a numerical solution, known solutions of the Vlasov equation are used. Such approach enables us to determine optimal relations between numerical method parameters to achieve the most efficiency of the algorithm. Refs 15. Figs 3. Tables 2.