I have a grid of units whose dynamics are said to be governed by the same differential equation. As I understand it, a differential equation describes how a given function is related to its derivative. In a situation like this, how do I simulate the units? If I know the parameters of each unit, I could solve the differential equation, and there would be nothing to simulate (just compute the function values ..)
Is there something I am missing? Could I, say, just initialize each unit to a random state and then update using the differential equation directly?