Kinetic and hyperbolic equations contain small scales (mean free path/time, Debye length,
relaxation or reaction time, etc.) that lead to various different asymptotic regimes, in which …

Monte Carlo is one of the most versatile and widely used numerical methods. Its
convergence rate, O (N− 1/2), is independent of dimension, which shows Monte Carlo to be …

In this survey we consider the development and mathematical analysis of numerical
methods for kinetic partial differential equations. Kinetic equations represent a way of …

Many kinetic models of the Boltzmann equation have a diffusive scaling that leads to the
Navier--Stokes type parabolic equations as the small scaling parameter approaches zero. In …

In this paper, we propose a general time-discrete framework to design asymptotic-
preserving schemes for initial value problem of the Boltzmann kinetic and related equations …

We propose a new numerical scheme for linear transport equations. It is based on a
decomposition of the distribution function into equilibrium and nonequilibrium parts. We also …

We consider implicit-explicit (IMEX) Runge--Kutta (RK) schemes for hyperbolic systems with
stiff relaxation in the so-called diffusion limit. In such a regime the system relaxes towards a …

Many transport equations, such as the neutron transport, radiative transfer, and transport
equations for waves in random media, have a diffusive scaling that leads to the diffusion …

We present new implicit-explicit (IMEX) Runge Kutta methods suitable for time dependent
partial differential systems which contain stiff and non stiff terms (ie convection-diffusion …

We consider the development of hyperbolic transport models for the propagation in space of
an epidemic phenomenon described by a classical compartmental dynamics. The model is …