@PhDThesis{ itlic:2005-010,
author = {Paul Sj{\"o}berg},
title = {Numerical Solution of the {F}okker-{P}lanck Approximation
of the Chemical Master Equation},
school = {Department of Information Technology, Uppsala University},
department = {Division of Scientific Computing},
year = {2005},
number = {2005-010},
type = {Licentiate thesis},
month = dec,
day = {15},
copies-printed= {84},
pages = {100},
abstract = {The chemical master equation (CME) describes the
probability for the discrete molecular copy numbers that
define the state of a chemical system. Each molecular
species in the chemical model adds a dimension to the state
space. The CME is a difference-differential equation which
can be solved numerically if the state space is truncated
at an upper limit of the copy number in each dimension. The
size of the truncated CME suffers from an exponential
growth for an increasing number of chemical species.
In this thesis the chemical master equation is approximated
by a continuous Fokker-Planck equation (FPE) which makes it
possible to use sparser computational grids than for CME.
FPE on conservative form is used to compute steady state
solutions by computation of an extremal eigenvalue and the
corresponding eigenvector as well as time-dependent
solutions by an implicit time-stepping scheme.
The performance of the numerical solution is compared to a
standard Monte Carlo algorithm. The computational work for
a solutions with the same estimated error is compared for
the two methods. Depending on the problem, FPE or the Monte
Carlo algorithm will be more efficient. FPE is well suited
for problems in low dimensions, especially if high accuracy
desirable.}
}