IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-319-60300-1_4.html
   My bibliography  Save this book chapter

Solution Methods of Master Equations

In: Modelling with the Master Equation

Author

Listed:
  • Günter Haag

    (University of Stuttgart, Institute of Theoretical Physics II)

Abstract

After the derivation of the Master equation, it is logical to introduce and discuss different methods of its solution. One obvious and frequently applied method consists in the approximate transformation of the discrete Master equation in a partial differential equation, namely the Fokker–Planck equation. The not so well-known T-factor method is very efficient in the transformation of the Master equation into difference equations of reduced order, which are easier to handle, and into continued fractions. This method also provides a very elegant way to derive exact and approximate stationary solutions of the Master equation, even in case when detailed balance is not fulfilled. A general graph-theoretical method for the stationary solution developed by Kirchhoff for electrical networks is also presented. In case of detailed balance an exact solution method for the stationary probability distribution is also presented. The chapter closes with exact and approximate solution methods for one-dimensional Master equations with two particle jumps.

Suggested Citation

  • Günter Haag, 2017. "Solution Methods of Master Equations," Springer Books, in: Modelling with the Master Equation, chapter 0, pages 63-91, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-60300-1_4
    DOI: 10.1007/978-3-319-60300-1_4
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-3-319-60300-1_4. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.