This is an electronic analogue of the Finite Volume Method for integrating differential equations. In this case it’s simulating a very simple advection equation with diffusion. You can think of it as simulating the flow of dye through a constant velocity stream. The voltage of each capacitor represents the quantity of dye at that point. Due to the simple flux (dye flow rate) determination method (taking the flux between each volume to be the average of the values of the two volumes) the advection alone is unstable. As such, I have added 500Ω resistors to add diffusion to the advection. The value 500Ω is a critical value and increasing the resistance beyond that reveals the instability. With no resistors at all (infinite resistance, no diffusion) and the switch closed only every other capacitor becomes charged. Reducing the resistance from infinity (adding diffusion) counteracts this instability and works to balance the charges on the capacitors. At 500Ω exactly it completely eliminates the instability. Any more resistance and the capacitors won’t all have the same charge during steady-state operation.
