Which type of simulation involves variables changing continuously over time?

The type of simulation that involves variables changing continuously over time is continuous simulation. This approach is designed to model systems where changes occur in a smooth and uninterrupted fashion, allowing for the analysis of complex behaviors over time.

In continuous simulation, the state of the system is represented by a set of differential equations that describe how the variables interact and change. This is particularly useful in scenarios such as fluid dynamics, population models, or any context where the variables of interest evolve without discrete jumps.

In contrast, other types of simulations focus on situations where changes occur at specific intervals or events. Discrete event simulation, for example, centers around modeling systems as sequences of events that happen at distinct points in time, making it less suited for continuously changing variables. Static simulation does not involve time or changes at all but instead examines a fixed scenario at a specific point. Random simulation typically introduces elements of chance and randomness into the modeling process but does not focus on continuous changes in variables.

Understanding the nature of continuous simulation allows for better modeling of systems that reflect real-world dynamics wherein changes are gradual and evolving rather than sudden or occasional.