Dear all,
I am trying to solve the Fokker-Planck equation
$$\tau \frac{\partial P(v,t)}{\partial t} = \frac{\sigma^{2}}{2}\frac{\partial^{2}P(v,t)}{\partial v^{2}} + \frac{\partial }{\partial v}\left((v-\mu)P(v,t)\right))$$
subject to the boundary conditions
$$ P(v_{t},t) = 0 $$
and
$$ P(v_{r}^{-},t) = P(v_{r}^{+},t) $$
as well as
$$ \frac{\partial P}{\partial v}(v_{r}^{-},t)-\frac{\partial P}{\partial v}(v_{r}^{+},t)= \frac{\partial P}{\partial v} (v_{t},t).$$
Here, $+$ and $-$ denote the right and left limit, respectively.
The domain of solution is the interval $$ \mathcal D = [v_{r},v_{t}].$$ I am both stuck with the weak formulation as well as the implementation of the jump boundary condition.
Many thanks for your help.
