On Feb 23, 2010, at 10:06 AM, John-Oliver Engler wrote:
I have a stiff stochastic differential equation (SDE) of second
order in time that I have already implemented. We are hence talking
about a 2d stiff stochastic dynamical system being equivalent to the
original SDE.
Now, I want to study the corresponding Fokker-Planck Equation (FPE)
- which is a partial differential equation - to learn about the time
evolution of the probability density of the system. I want to do
this with FiPy which I have already used in a much easier case.
Under the assumption that a stiff SDE has also a stiff FPE, can I
use FiPy for this? Do you have any experiences with that?
Experience with Fokker-Planck and stochastics, per se? No.
FiPy is quite capable of solving convection-diffusion problems,
though, and we've done a little bit with Langevin noise terms (see the
documentation for the GaussianNoiseTerm).
A natural way would be to use only implicit schemes which are known
to be more stable in case of stiff equations but I am not sure if
just typing ImplicitDiffusionTerm(...) leads to stable results,
hence the question for experiences already made using FiPy in such a
case.
FiPy uses implicit schemes by default, which as you say, are certainly
more stable than explicit schemes. Things like coupling between
equations, non-linear coefficients, and shocks can severely degrade
how easily your equations are solved. It's all very problem specific.
