A computer simulation or a computer model is a computer program which attempts to simulate an abstract model of a particular system. Computer simulations have become a useful part of modeling many natural systems in physics, chemistry and biology, human systems in economics and social science and in the process of engineering new technology, to gain insight into the operation of those systems. Traditionally, the formal modeling of systems has been via a mathematical model, which attempts to find analytical solutions to problems which enables the prediction of the behaviour of the system from a set of parameters and initial conditions. Computer simulations build on, and are a useful adjunct to purely mathematical models in science and technology and entertainment.
History
Computer simulation was developed handinhand with the rapid growth of the computer, following its first largescale deployment during the Manhattan Project in World War II to model the process of nuclear detonation. It was a simulation of 12 hard spheres using a Monte Carlo algorithm. Computer simulation is often used as an adjunct to, or substitution for, modeling systems for which simple closed form analytic solutions are not possible. There are many different types of computer simulation; the common feature they all share is the attempt to generate a sample of representative scenarios for a model in which a complete enumeration of all possible states of the model would be prohibitive or impossible. Computer models were initially used as a supplement for other arguments, but their use later became rather widespread. The physicist Richard Feynman, was not fond of such models and once called them "a disease".
Types of computer simulation
Computer models can be classified according to several criteria including:
For example:

Stochastic models use random number generators to model the chance or random events; they are also called Monte Carlo simulations.
 A discrete event simulation (DE) manages events in time. Most computer, logictest and faulttree simulations are of this type. In this type of simulation, the simulator maintains a queue of events sorted by the simulated time they should occur. The simulator reads the queue and triggers new events as each event is processed. It is not important to execute the simulation in real time. It's often more important to be able to access the data produced by the simulation, to discover logic defects in the design, or the sequence of events.
 A continuous simulation uses differential equations (either partial or ordinary), implemented numerically. Periodically, the simulation program solves all the equations, and uses the numbers to change the state and output of the simulation. Most flight and racingcar simulations are of this type. This may also be used to simulate electrical circuits. Originally, these kinds of simulations were actually implemented on analog computers, where the differential equations could be represented directly by various electrical components such as opamps. By the late 1980s, however, most "analog" simulations were run on conventional digital computers that emulate the behavior of an analog computer.
 A special type of discrete simulation which does not rely on a model with an underlying equation, but can nonetheless be represented formally, is agentbased simulation. In agentbased simulation, the individual entities (such as molecules, cells, trees or consumers) in the model are represented directly (rather than by their density or concentration) and possess an internal state and set of behaviors or rules which determine how the agent's state is updated from one timestep to the next.

distributed models run on a network of interconnected computers, possibly through the Internet. Simulations dispersed across multiple host computers like this are often referred to as "distributed simulations". There are several military standards for distributed simulation, including Aggregate Level Simulation Protocol (ALSP), Distributed Interactive Simulation (DIS) and the High Level Architecture (HLA).
Computer simulation in science
Examples of types of computer simulations in science, which are derived from an underlying mathematical description:
Examples of other types of simulations:
 agent based simulation has been used effectively in ecology, where it is often called individual based modeling and has been used in situations for which individual variability in the agents cannot be neglected, such as population dynamics of salmon and trout (most purely mathematical models assume all trout behave identically).
Notable, and sometimes controversial, computer simulations used in science include: Donella Meadows' World3 used in the Limits to Growth, James Lovelock's Daisyworld and Thomas Ray's Tierra.
Computer simulation in practical contexts
In engineering and practical contexts, it's often very important to display the results of a simulation in real time, to provide a realistic simulation for the trainee or gamer. When computer graphics are used for such a purpose, this falls into the domain of scientific visualization.
See also