Fig. 4.

a Errors $e_m(k)$ and $e_v(k)$ given by Eq. (13) are computed at time $50\mathrm{s}$. b The maximum absolute values of the errors $e_m(k)$ and $e_v(k)$ given by Eq. (13) are computed at time $50\mathrm{s}$ with a static boundary and different values of $\alpha$. The maximum value of the errors is taken over all region, $\Omega$. Red and green lines are relative errors of the means and standard deviations between the analytic solution of the Markov chain model and Scheme 1. Blue and purple lines are relative errors between the Markov chain model and Scheme 2 (Color figure online)