@TechReport{ it:2004-054,
author = {Lars Ferm and Per L{\"o}tstedt and Paul Sj{\"o}berg},
title = {Adaptive, Conservative Solution of the {F}okker-{P}lanck
Equation in Molecular Biology},
institution = {Department of Information Technology, Uppsala University},
department = {Division of Scientific Computing},
year = {2004},
number = {2004-054},
month = nov,
abstract = {The Fokker-Planck equation on conservation form is
discretized by a finite volume method and advanced in time
by a linear multistep method. The grid cells are refined
and coarsened in blocks of the grid depending on an
estimate of the spatial discretization error and the time
step is chosen to satisfy a tolerance on the temporal
discretization error. The solution is conserved across the
block boundaries so that the total probability is constant.
A similar effect is achieved by rescaling the solution. The
steady state solution is determined as the eigenvector
corresponding to the zero eigenvalue. The method is applied
to the solution of a problem with two molecular species and
the simulation of a circadian clock. Comparison is made
with a stochastic method.}
}