Positive Second Order Finite Difference Methods on Fokker-Planck Equations with Dirac Initial Data

8 Pages Posted: 13 Jul 2017

Date Written: April 29, 2015

Abstract

The backward Euler scheme is known to be monotone and positivity preserving. Those are particularly important properties when the partial differential equation represents a density with a discontinuous initial condition like a Dirac. Many schemes will produce oscillations or negative densities. This paper analyzes the behavior of a few simple schemes related to backward Euler, namely BDF2, and Lawson-Morris on the specific problem of a diffusion with Dirac initial condition.

Keywords: Euler, Dirac, BDF2, Richardson extrapolation, Crank-Nicolson, finite difference

JEL Classification: C00, C60, C61, C63

Suggested Citation

Le Floc'h, Fabien, Positive Second Order Finite Difference Methods on Fokker-Planck Equations with Dirac Initial Data (April 29, 2015). Available at SSRN: https://ssrn.com/abstract=2600500 or http://dx.doi.org/10.2139/ssrn.2600500

Fabien Le Floc'h (Contact Author)

Calypso Technology ( email )

106 rue de la Boetie
Paris, 75008
France

Independent ( email )

France

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