Accretion disc is formed from a massive cloud of gas and dust in the space due to gravitation.
Examples are galaxies and solar systems. The aim of the work is to create the mathematical model of the disc evolution. That means to develope parallel numerical methods for solution of equations describing the dynamics of matter in the disc. They are Poisson and Vlasov-Liouville equations. In order to solve the Vlasov-Liouville equation PIC method is applied.