There are alternatives to using op amp based integrators and differentiators. As long as systems can be described by a reasonable set of equations, simulation using digital computers is possible. The primary advantages of a digital computer-based simulation scheme is that it is very flexible and potentially very accurate. Before the rise of affordable and powerful desktop digital computers, the speed of response of the digital technique was a severe limitation. Analog computers can be configured as real-time or faster-than-real-time devices: they respond at the same speed or faster than the system that is being simulated. The typically heavy computation load of the digital computer requires prodigious calculation speed to keep up with reasonably fast processes. Fortunately, this is no longer the problem it once was. Another advantage of the analog computer is its immediacy. It is by nature, interactive. This means that an operator can change simulation parameters and immediately see the result. Finally, there are some applications for which the added cost of the computing hardware cannot be justified. If these are not issues, then a digital-based simulation will most likely be preferred. The general idea is to calculate the response for several closely spaced points in time. The results may be used in a variety of ways. For example, graphs may be created that can then be studied at leisure or the resulting digital signal may be used elsewhere in the system. An extreme (although generally impractical) possibility is to design an op amp based simulator and then simulate its response by using a digital circuit simulator! As you might guess, this double simulation is not particularly efficient, especially with large systems.