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The Fokker-Planck Equation

Methods of Solution and Applications

  • Hannes Risken

Part of the Springer Series in Synergetics book series (SSSYN, volume 18)

Table of contents

  1. Front Matter
    Pages I-XIV
  2. Hannes Risken
    Pages 1-12
  3. Hannes Risken
    Pages 13-31
  4. Hannes Risken
    Pages 32-62
  5. Hannes Risken
    Pages 63-95
  6. Hannes Risken
    Pages 163-178
  7. Hannes Risken
    Pages 179-195
  8. Hannes Risken
    Pages 229-275
  9. Hannes Risken
    Pages 276-373
  10. Hannes Risken
    Pages 374-413
  11. Back Matter
    Pages 414-454

About this book

Introduction

One of the central problems synergetics is concerned with consists in the study of macroscopic qualitative changes of systems belonging to various disciplines such as physics, chemistry, or electrical engineering. When such transitions from one state to another take place, fluctuations, i.e., random processes, may play an im­ portant role. Over the past decades it has turned out that the Fokker-Planck equation pro­ vides a powerful tool with which the effects of fluctuations close to transition points can be adequately treated and that the approaches based on the Fokker­ Planck equation are superior to other approaches, e.g., based on Langevin equa­ tions. Quite generally, the Fokker-Planck equation plays an important role in problems which involve noise, e.g., in electrical circuits. For these reasons I am sure that this book will find a broad audience. It pro­ vides the reader with a sound basis for the study of the Fokker-Planck equation and gives an excellent survey of the methods of its solution. The author of this book, Hannes Risken, has made substantial contributions to the development and application of such methods, e.g., to laser physics, diffusion in periodic potentials, and other problems. Therefore this book is written by an experienced practitioner, who has had in mind explicit applications to important problems in the natural sciences and electrical engineering.

Keywords

Fourier transform Potential computer simulation differential equation diffusion distribution function eigenvalue numerical method ordinary differential equation partial differential equation path integral solution stochastic process susceptibility synergetics

Authors and affiliations

  • Hannes Risken
    • 1
  1. 1.Abteilung für Theoretische PhysikUniversität UlmUlmFed. Rep. of Germany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-96807-5
  • Copyright Information Springer-Verlag Berlin Heidelberg 1984
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-96809-9
  • Online ISBN 978-3-642-96807-5
  • Series Print ISSN 0172-7389
  • Buy this book on publisher's site
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