Approximation of the Fokker-Planck equation of the stochastic chemostat

作者：Campillo Fabien^*; Joannides Marc; Larramendy Valverde Irene

来源：Mathematics and Computers in Simulation, 2014, 99: 37-53.

DOI：10.1016/j.matcom.2013.04.012

• Chemostat
• Stochastic differential equation
• Fokker-Planck equation
• Finite difference scheme

We consider a stochastic model of the two-dimensional chemostat as a diffusion process for the concentration of substrate and the concentration of biomass. The model allows for the washout phenomenon: the disappearance of the biomass inside the chemostat. We establish the Fokker-Planck equation associated with this diffusion process, in particular we describe the boundary conditions that modelize the washout. We propose an adapted finite difference scheme for the approximation of the solution of the Fokker-Planck equation.

• 出版日期2014-5
• 单位INRIA