Difference Schemes for the Time Evolution of Three-Dimensional Kinetic Equations

This paper is devoted to the development of finite difference methods for the solution of problems involving the three-dimensional kinetic equation with a Coulomb collision operator. New conservative difference schemes are presented and analysed. The schemes include a new approximation for mixed derivatives and accurate treatment of internal separatrix layers. The main advantages of the new schemes are improved stability and accuracy which, for example, allows calculation of the ion distribution function in thermonuclear experiments for a wider range of parameters.