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Stochastic Numerics for the Boltzmann Equation [electronic resource] / by Sergej Rjasanow, Wolfgang Wagner.

By: Rjasanow, Sergej [author.].
Contributor(s): Wagner, Wolfgang [author.] | SpringerLink (Online service).
Material type: TextTextSeries: Springer Series in Computational Mathematics: 37Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2005Description: XIV, 256 p. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783540276890.Subject(s): Numerical analysis | Distribution (Probability theory | Differential equations, partial | Numerical Analysis | Probability Theory and Stochastic Processes | Theoretical, Mathematical and Computational Physics | Partial Differential EquationsAdditional physical formats: Printed edition:: No title; Printed edition:: No title; Printed edition:: No titleDDC classification: 518 Online resources: Click here to access online
Contents:
Kinetic theory -- Related Markov processes -- Stochastic weighted particle method -- Numerical experiments.
In: Springer eBooksSummary: 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.
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Kinetic theory -- Related Markov processes -- Stochastic weighted particle method -- Numerical experiments.

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.

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