Higher Order Approximation Methods for the Boltzmann Equation

Time step truncation error in direct simulation Monte Carlo

“…In the variant proposed in Ref. 10, during a single iteration: particles move for a half time step; collisions are evaluated for a full time step; particles move again for a half time step; and statistical samples are measured. The accuracy of statistical samples taken between iteration points may improve because the sampling is time-centered.…”

Fast Spectral Methods for the Fokker–Planck–Landau Collision Operator

“…A very common and simple scheme is Strang splitting [32], which gives second order in time. This approach has been used for the numerical solution of the Boltzmann equation in [23].…”

High order numerical methods for the space non-homogeneous Boltzmann equation

“…Recently, second order splitting algorithms for Boltzmann like equations were also presented in [15]. Although higher order splitting strategies are available, in practice they are seldom used because of stability problems.…”