We will survey some recent results for solvers of Boltzmann and Vlasov Maxwell systems as well as qualitative phenomena of the simulations. More specifically, we'll look at the problem of recurrence and positivity propagation for high order discontinuous Galerkin (DG) schemes, conservation, stability and error estimates as well as some numerical results such us BGK formation, both in the repulsive and attracting forces cases. We will briefly discuss the effect of strong external magnetic forces and the homogenization by gyro-kinetic averaging of Vlasov-Boltzmann-Maxwell resulting in a non-local drift effect due to collisions.
These are results that have been developed in a series of work in collaboration with Yingda Cheng, Fengyan Li, Phil Morrison and Mihai Bostan.
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