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- Clement Mouhot, Lorenzo Pareschi
- Math. Comput.
- 2006

The development of accurate and fast numerical schemes for the five-fold Boltzmann collision integral represents a challenging problem in scientific computing. For a particular class of interactions, including the so-called hard spheres model in dimension three, we are able to derive spectral methods that can be evaluated through fast algorithms. These… (More)

- Lorenzo Pareschi, Giovanni Russo
- SIAM J. Numerical Analysis
- 2000

- Lorenzo Pareschi, Giovanni Russo
- J. Sci. Comput.
- 2005

We consider implicit-explicit (IMEX) Runge Kutta methods for hyperbolic systems of conservation laws with stiff relaxation terms. The explicit part is treated by a strong-stabilitypreserving (SSP) scheme, and the implicit part is treated by an L-stable diagonally implicit Runge Kutta (DIRK). The schemes proposed are asymptotic preserving (AP) in the zero… (More)

In this paper, we consider a simple kinetic model of economy involving both exchanges between agents and speculative trading. We show that the kinetic model admits non trivial quasi-stationary states with power law tails of Pareto type. In order to do this we consider a suitable asymptotic limit of the model yielding a Fokker-Planck equation for the… (More)

- Shi Jin, Lorenzo Pareschi, Giuseppe Toscani
- SIAM J. Numerical Analysis
- 2000

Many transport equations, such as the neutron transport, radiative transfer, and transport equations for waves in random media, have a diiusive scaling that leads to the diiusion equations. In many physical applications, the scaling parameter (mean free path) may diier in several orders of magnitude from the rareeed regimes to the hydrodynamic (diiusive)… (More)

- Lorenzo Pareschi, Giovanni Russo
- SIAM J. Scientific Computing
- 2001

- Giacomo Dimarco, Lorenzo Pareschi
- SIAM J. Numerical Analysis
- 2011

Abstract. We introduce a class of exponential Runge-Kutta integration methods for kinetic equations. The methods are based on a decomposition of the collision operator into an equilibrium and a non equilibrium part and are exact for relaxation operators of BGK type. For Boltzmann type kinetic equations they work uniformly for a wide range of relaxation… (More)

- Lorenzo Pareschi
- 2006

In [32, 31], fast deterministic algorithms based on spectral methods were derived for the Boltzmann collision operator for a class of interactions including the hard spheres model in dimension 3. These algorithms are implemented for the solution of the Boltzmann equation in dimension 2 and 3, first for homogeneous solutions, then for general non homogeneous… (More)

We present new implicit-explicit (IMEX) Runge Kutta methods suitable for time dependent partial differential systems which contain stiff and non stiff terms (i.e. convection-diffusion problems, hyperbolic systems with relaxation). Here we restrict to diagonally implicit schemes and emphasize the relation with splitting schemes and asymptotic preserving… (More)

- Lorenzo Pareschi
- SIAM J. Numerical Analysis
- 2001

Many applications involve hyperbolic systems of conservation laws with source terms. The numerical solution of such systems may be challenging, especially when the source terms are stiff. Uniform accuracy with respect to the stiffness parameter is a highly desirable property but it is, in general, very difficult to achieve using underresolved… (More)