Algorithm 1.

. Diffusion in one dimension with diffusion radius s=1

Choose s and ε
Calculated Δtmax as a function of ε, s, and κ=D∕l2
Choose Δt⩽Δtmax
whilet⩽tfinaldo
fori=1 to ndo
$\Delta X_{i(i+1)}=\mathcal{B}({\widehat{p}}_{i(i+1)}\left(\Delta t\right),X_i)$
$\Delta X_{i(i-1)}=\mathcal{B}(\frac{{\widehat{p}}_{i(i-1)}\left(\Delta t\right)}{1-{\widehat{p}}_{i(i+1)}\left(\Delta t\right)},X_i-\Delta X_{i(i+1)})$
end for
fori=1 to ndo
Xi=Xi−ΔXi(i+1)−ΔXi(i−1)+ΔX(i+1)i+ΔX(i−1)i
end for
t=t+Δt
end while