Before revision:  A numerical validation shows high quality of the  approximation even for low populations and coarse lattices , and excellent speed of convergence with increasing system sizes .
After revision:  A numerical validation shows high quality of the approximation even for low populations and coarse lattices . In addition, we confirm the computational advantage in using the PDE limit over a traditional ordinary differential equation limit where the lattice is modeled discretely, yielding speed-ups of up to two orders of magnitude .