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
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: Suggested Citation