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Modeling and Computational Methods for Kinetic Equations

  • Pierre Degond
  • Lorenzo Pareschi
  • Giovanni Russo

Table of contents

  1. Front Matter
    Pages i-xi
  2. Rarefied Gases

    1. Front Matter
      Pages 1-1
    2. Alì Giuseppe, Angelo Marcello Anile
      Pages 59-80
    3. Sergej Rjasanow
      Pages 81-115
    4. Francis Filbet, Giovanni Russo
      Pages 117-145
  3. Applications

    1. Front Matter
      Pages 169-169
    2. Axel Klar, Raimund Wegener
      Pages 219-258
    3. Lorenzo Pareschi, Giuseppe Toscani
      Pages 259-285
    4. Weizhu Bao, Lorenzo Pareschi, Peter A. Markowich
      Pages 287-320
    5. Philippe Laurençot, Stéphane Mischler
      Pages 321-356

About this book

Introduction

In recent years kinetic theory has developed in many areas of the physical sciences and engineering, and has extended the borders of its traditional fields of application. New applications in traffic flow engineering, granular media modeling, and polymer and phase transition physics have resulted in new numerical algorithms which depart from traditional stochastic Monte--Carlo methods.

This monograph is a self-contained presentation of such recently developed aspects of kinetic theory, as well as a comprehensive account of the fundamentals of the theory. Emphasizing modeling techniques and numerical methods, the book provides a unified treatment of kinetic equations not found in more focused theoretical or applied works.

The book is divided into two parts. Part I is devoted to the most fundamental kinetic model: the Boltzmann equation of rarefied gas dynamics. Additionally, widely used numerical methods for the discretization of the Boltzmann equation are reviewed: the Monte--Carlo method, spectral methods, and finite-difference methods. Part II considers specific applications: plasma kinetic modeling using the Landau--Fokker--Planck equations, traffic flow modeling, granular media modeling, quantum kinetic modeling, and coagulation-fragmentation problems.

Modeling and Computational Methods of Kinetic Equations will be accessible to readers working in different communities where kinetic theory is important: graduate students, researchers and practitioners in mathematical physics, applied mathematics, and various branches of engineering. The work may be used for self-study, as a reference text, or in graduate-level courses in kinetic theory and its applications.

Keywords

Approximation algorithm algorithms mathematical physics modeling numerical methods numerics operator

Editors and affiliations

  • Pierre Degond
    • 1
  • Lorenzo Pareschi
    • 2
  • Giovanni Russo
    • 3
  1. 1.Department of MathematicsUniversité Paul SabatierToulouse CedexFrance
  2. 2.Department of MathematicsUniversità di FerraraFerraraItaly
  3. 3.Università di CataniaCataniaItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-8176-8200-2
  • Copyright Information Birkhäuser Boston 2004
  • Publisher Name Birkhäuser, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-6487-3
  • Online ISBN 978-0-8176-8200-2
  • Series Print ISSN 2164-3679
  • Buy this book on publisher's site
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