Table 1.

Pseudocode for the multiscale reaction–diffusion algorithm with Scheme 1 applied to simulation of diffusion

[A]	Set $t=0$ and $t_s=\Delta t$. Initialize species numbers, $\mathbf{X}(0)$, in ${\Omega }_m$ and ${\Omega }_s$. Then, generate random numbers $r_1$ and $r_2$ uniformly distributed in (0, 1). Set $\tau$ so that $\tau =-a_0^{-1}log\left(r_1\right)$, where $a_0$ is defined in Eq. (11). Set the next time when the diffusion occurs in ${\Omega }_m$ as $t_m=\tau$
[B]	If $t_m\le t_s$
	$\bullet$ Set $t=t_m$
	$\bullet$ Use $r_2$ to determine which diffusive jump occurs. Each diffusive jump to the left (resp. to the right) has the probability $a_{-,i}^k/a_0$ (resp. $a_{+,i}^k/a_0$) to occur
	$\bullet$ If the selected diffusive jump only includes internal compartments in ${\Omega }_m$, update species numbers in the corresponding compartments
	$\bullet$ If the diffusion occurs across the interface from ${\Omega }_m$ to ${\Omega }_s$, update the species number in $C_{K_s}$ by transferring one molecules from $C_{K_s+1}$ to the corresponding grid point in ${\Omega }_s$
	$\bullet$ If the diffusion occurs across the interface from ${\Omega }_s$ to ${\Omega }_m$, update the species number in $C_{K_s+1}$ by adding one molecule and subtracting one from the corresponding grid point in ${\Omega }_s$
	$\bullet$ Generate random numbers $r_1$ and $r_2$ uniformly distributed in (0, 1). Set $\tau$ so that $\tau =-a_0^{-1}log\left(r_1\right)$, where $a_0$ is defined in Eq. (11). Set the next time when the diffusion occurs in ${\Omega }_m$ as $t_m=t+\tau$
[C]	If $t_s\le t_m$
	$\bullet$ Set $t=t_s$
	$\bullet$ Use Eq. (12) to update the SPDE part of the system from t to $t+\Delta t$
	$\bullet$ Set the next time of the update of the SPDE part as $t_s=t+\Delta t$
[D]	Repeat steps [B]–[C] until the simulation ends