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Numerical approach to the fractional Klein-Kramers equation

Marcin Magdziarz* and Aleksander Weron

  • Hugo Steinhaus Center, Institute of Mathematics and Computer Science, Wroclaw University of Technology, Wyb. Wyspianskiego 27, 50-370 Wroclaw, Poland

  • *marcin.magdziarz@pwr.wroc.pl
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Phys. Rev. E 76, 066708 – Published 26 December, 2007

DOI: https://doi.org/10.1103/PhysRevE.76.066708

Abstract

Subdiffusion in the presence of an external force field can be described in phase space by the fractional Klein-Kramers equation. In this paper, we explore the stochastic structure of this equation. Using a subordination method, we define a random process whose probability density function is a solution of the fractional Klein-Kramers equation. The structure of the introduced process agrees with the two-stage scenario underlying the anomalous diffusion mechanism, in which trapping events are superimposed on the Langevin dynamics. We develop an efficient computer algorithm for visualization of fractional Klein-Kramers dynamics and present some simulation results based on Monte Carlo techniques.

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Outline

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Phys. Rev. E 76, 066708– Published 26 December, 2007
  • Received 13 August 2007

© 2007 American Physical Society

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