I'm working on the random walk process of particles to compare with a pde solution. I understand the random walk algorithm for each particle's location at each time with the Neumann boundary condition. However, I don't see how to implement the random walk algorithm with the Robin(or mixed) boundary condition.
For example, we can consider the 1d convection-diffusion equation \begin{align*} u_{t} + (c(x)u)_{x} = Du_{xx}, \qquad x\in [0,L], \;\ t\geq 0 \end{align*} with a Robin boundary condition \begin{align*} \frac{\partial u}{\partial n} = k u, \qquad x = 0 , L. \end{align*}