Numerical methods for plasma physics in collisional regimes

We consider the development of accurate and efficient numerical methods for the solution of the Vlasov-Landau equation describing a collisional plasma. The methods combine a Lagrangian approach for the Vlasov solver with a fast spectral method for the solution of the Landau operator. To this goal, new modified spectral methods for the Landau integral which are capable to capture correctly the Maxwellian steady state are introduced. A particular care is devoted to the construction of Implicit-Explicit and Exponential Runge-Kutta methods that permit to achieve high-order and efficient time integration of the collisional step. Several numerical tests are reported which show the high accuracy of the numerical schemes here presented.