Continuous Simulations on Computers

Question

A digital computer is a discrete system. So, does it follow that a continuous model cannot be simulated on a digital computer? It appears that only an approximation of a continuous model via a discrete simulation is possible. From what I've read this seems to be the case, but I wanted to get some feedback/input from others on the topic.

I did find this while searching around for further information on this topic:

Continuous simulation is something that can only really be accomplished with an analog computer. Using a digital computer one can approximate a continuous simulation by making the time step of the simulation sufficiently small so there are no transitions within the system between time steps. The premise for a continuous simulation is that there is a continuous time flow and the simulation is stepped in time increments. ¹

I also thought this made a good point about approximating via a discrete simulation:

In some systems the state changes all the time, not just at the time of some discrete events. For example, the water level in a reservoir with given in and outflows may change all the time. In such cases "continuous simulation" is more appropriate, although discrete event simulation can serve as an approximation. ²

¹ Continuous Simulation - http://www.systems-thinking.org/simulation/contsim.htm
² Modeling & Simulation - http://home.ubalt.edu/ntsbarsh/simulation/sim.htm

Thanks for the input.

Answer 1

You may not be able to perfectly simulate a continuous system using a digital computer, but I have two thoughts on the idea of modeling or simulating continuous systems:

1. "does it follow that a continuous model cannot be simulated on a digital computer?" For what purpose? Can it be perfectly and flawlessly simulated such that you have an exact digital representation of a continuous process? Probably not. But as you yourself have noted, discrete processes may approximate the continuous process adequately enough that it simply doesn't matter.
2. Is the process actually continuous? I've found in modeling in my field I run across far more processes modeled as continuous ones when they should be discrete (usually to take advantage of easier analytic techniques and readily available ODE solvers) than continuous models suffering from inadequate discrete approximations.