Comparison between fixed and Gaussian steplength in Monte Carlo simulations for diffusion processes

  • Authors:

  • V. Ruiz Barlett;M. Hoyuelos;H. O. Mártin

  • Affiliations:

  • Instituto de Investigaciones Físicas de Mar del Plata (CONICET-UNMdP), Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, Funes 3350 ...;Instituto de Investigaciones Físicas de Mar del Plata (CONICET-UNMdP), Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, Funes 3350 ...;Instituto de Investigaciones Físicas de Mar del Plata (CONICET-UNMdP), Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, Funes 3350 ...

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2011

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Abstract

We analyze the different degrees of accuracy of two Monte Carlo methods for the simulation of one-dimensional diffusion processes with homogeneous or spatial dependent diffusion coefficient that we assume correctly described by a differential equation. The methods analyzed correspond to fixed and Gaussian steplengths. For a homogeneous diffusion coefficient it is known that the Gaussian steplength generates exact results at fixed time steps @Dt. For spatial dependent diffusion coefficients the symmetric character of the Gaussian distribution introduces an error that increases with time. As an example, we consider a diffusion coefficient with constant gradient and show that the error is not present for fixed steplength with appropriate asymmetric jump probabilities.