Stochastic Numerics for the Boltzmann Equation

  • Sergej Rjasanow
  • Wolfgang Wagner

Part of the Springer Series in Computational Mathematics book series (SSCM, volume 37)

Table of contents

  1. Front Matter
    Pages I-XIII
  2. Pages 1-32
  3. Pages 147-210
  4. Back Matter
    Pages 211-256

About this book


Stochastic numerical methods play an important role in large scale computations in the applied sciences. The first goal of this book is to give a mathematical description of classical direct simulation Monte Carlo (DSMC) procedures for rarefied gases, using the theory of Markov processes as a unifying framework. The second goal is a systematic treatment of an extension of DSMC, called stochastic weighted particle method. This method includes several new features, which are introduced for the purpose of variance reduction (rare event simulation). Rigorous convergence results as well as detailed numerical studies are presented.


Boltzmann equation Monte Carlo methods Variance interacting particle systems numerics rarified gas dynamics stochastic numerics

Authors and affiliations

  • Sergej Rjasanow
    • 1
  • Wolfgang Wagner
    • 2
  1. 1.Fachrichtung 6.1 — MathematikUniversität des SaarlandesSaarbrückenGermany
  2. 2.Weierstrass Institute for Applied Analysis and StochasticsBerlinGermany

Bibliographic information

Industry Sectors
Energy, Utilities & Environment