Hermite spectral method for Fokker-Planck-Landau equation modeling collisional plasma

We propose an Hermite spectral method for the Fokker-Planck-Landau (FPL) equation. Both distribution functions and collision terms are approximated by series expansions of functions. To handle complexity quadratic FPL operator, a reduced model is built adopting operator lower-order diffusive Fokker-Planck higher-order in expansion operator. The numerical scheme split into three steps according to Strang splitting, where different centers employed take advantage standard normalized basis [36] adopted during convection utilize precalculated coefficients terms, while one constituted local macroscopic velocity temperature utilized acceleration step, which effect external force can be simplified ODE. Projections between achieved algorithm proposed [29]. Several examples studied test validate our new method.