The completely conservative difference schemes for the nonlinear Landau-Fokker-Planck equation

Conservativity and complete conservativity of finite difference schemes are considered in connection with the nonlinear kinetic Landau-Fokker-Planck equation. The characteristic feature of this equation is the presence of several conservation laws. Finite difference schemes, preserving density and energy are constructed for the equation in one- and two-dimensional velocity spaces. Some general methods of constructing such schemes are formulated. The constructed difference schemes allow us to carry out the numerical solution of the relaxation problem in a large time interval without error accumulation. An illustrative example is given.