Papers Submitted
Author's Comments:
Submitted to the SIAM Journal of Numerical Analysis, August 2007
Abstract:
When immune cells detect foreign molecules, they secrete soluble
factors that attract other immune cells to the site of the infection.
In this paper, I study numerical solutions to a model of this behavior
proposed by Kepler. In this model the soluble factors are governed by
a system of reaction-diffusion equations with sources that are
centered on the cells. The motion of the model cells is a Langevin process
that is biased toward the gradient of the soluble factors. I have shown
that the solution to this system exists for all time and remains
positive, the supremum is a priori bounded and the derivatives are
bounded for finite time. I have also developed a first order split
scheme for solving the reaction-diffusion stochastic system. This
allows us to make use of known first order schemes for solving the
diffusion, the reaction and the stochastic differential equations
separately.
Keywords:
operator splitting • reaction-diffusion • stochastic differential equations