I want to simulate a system of random walkers (called A) with diffusion coefficient equal to D and other systems of random walkers (called type B) with diffusion coefficient equal to 1000 D. Second type of walkers are smaller than the first ones and are eaten by the first type. As diffusion coefficient of B walkers are much bigger than the first type, I don't know how to choose the time step and space step of the simulation. Could anyone help? The small walkers perform a discrete random walk on a lattice and the big ones are described by a Wiener process. Also, big walkers move to the direction of the gradient of small walkers and they have a velocity which pushes them in a preferred direction of their body
In general, the only harm a small step size causes is that it costs runtime. Therefore the step size imposed by your small random walkers is a reasonable choice. The only reason why it wouldn’t be is that you need an even smaller step size, but I can only see that happening if:
- The velocity of your big walkers is not much smaller than the velocity of your small walkers.
- The concentration of your small walkers is inhomogeneous on scales of the movement of a big walker during one step (which should not happen unless it is imposed as an initial condition).
- The eating rate of your big walkers is so large that they eat a relevant portion of small walkers during one time step.
So, with other words, you should ensure that no considerable changes happen during one time step.