Numerical and analytical method for solving the two-dimensional kinetic Landau equation in self-similar variables

A stable method for numerical solution of a two-dimensional parabolic equation with a small parameter at the higher derivative is proposed. The method is based on splitting the equation in physical processes, moreover one of split equations obtained is solved analytically and the other equation -numerically. On the proposed method base is solved the Landau two-dimensional collisional kinetic equation in self-similar variables. The equation describes the longitudinal conductivity of electrons with account for the temperature gradient and ambipolar electric field. 12 refs., 1 fig