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Journal of Numerical Mathematics

Editor-in-Chief: Hoppe, Ronald H. W. / Kuznetsov, Yuri

Managing Editor: Olshanskii, Maxim

Editorial Board Member: Benzi, Michele / Brenner, Susanne C. / Carstensen, Carsten / Dryja, M. / Feistauer, Miloslav / Glowinski, R. / Lazarov, Raytcho / Nataf, Frédéric / Neittaanmaki, P. / Bonito, Andrea / Quarteroni, Alfio / Guzman, Johnny / Rannacher, Rolf / Repin, Sergey I. / Shi, Zhong-ci / Tyrtyshnikov, Eugene E. / Zou, Jun / Simoncini, Valeria / Reusken, Arnold

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Volume 23, Issue 3 (Sep 2015)

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Analysis of the Chang–Cooper discretization scheme for a class of Fokker–Planck equations

Masoumeh Mohammadi
  • Institut für Mathematik, Universität Würzburg, Campus Hubland Nord, Emil-Fischer-Str. 30, 97074 Würzburg, Germany
/ Alfio Borzì
  • Institut für Mathematik, Universität Würzburg, Campus Hubland Nord, Emil-Fischer-Str. 30, 97074 Würzburg, Germany. E-mail
  • Email:
Published Online: 2015-11-03 | DOI: https://doi.org/10.1515/jnma-2015-0018

Abstract

The Chang-Cooper discretization scheme for a class of Fokker-Planck equations is investigated. These equations of parabolic type govern the time evolution of the probability density function of stochastic processes, such that positivity of the density function and conservativeness of the total probability is guaranteed. It is shown that the Chang-Cooper scheme combined with backward first- and second-order finite differencing in time provides stable and accurate solutions that are conservative and positive. These properties are theoretically proven and validated by numerical experiments.

Keywords : Fokker-Planck equation; finite-difference discretization; accuracy and stability analysis

About the article

Received: 2013-12-09

Accepted: 2014-05-08

Published Online: 2015-11-03

Published in Print: 2015-09-01



Citation Information: Journal of Numerical Mathematics, ISSN (Online) 1569-3953, ISSN (Print) 1570-2820, DOI: https://doi.org/10.1515/jnma-2015-0018. Export Citation

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[1]
Lars Grüne
Jahresbericht der Deutschen Mathematiker-Vereinigung, 2016, Volume 118, Number 1, Page 3

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