Continuous simulation

Continuous Simulation refers to simulation approaches where a system is modeled with the help of variables that change continuously according to a set of differential equations. It is notable as one of the first uses ever put to computers, dating back to the Eniac in 1946. Continuous simulation allows prediction of rocket trajectories hydrogen bomb dynamics (N.B. this is the first use ever put to the Eniac) electric circuit simulation robotics Established in 1952, the Society for Modeling and Simulation International (SCS) is a nonprofit, volunteer-driven corporation dedicated to advancing the use of modeling & simulation to solve real-world problems. Their first publication strongly suggested that the Navy was wasting a lot of money through the inconclusive flight-testing of missiles, but that the Simulation Councils analog computer could provide better information through the simulation of flights. Since that time continuous simulation has been proven invaluable in military and private endeavors with complex systems. No Apollo moon shot would have been possible without it. The distinction between continuous and discrete applies both to real-world dynamic systems and to their simulation. A (real-world) dynamic system may be continuous or discrete. Continuous dynamic systems (like physical systems with material objects moving in space) are characterized by state variables the values of which change continuously, while the state variable values of discrete dynamic systems (like predator-prey ecosystems) "jump", that is, they are changed at discrete time steps only. In continuous simulation, continuously changing state variables of a system are modeled by differential equations. However, in digital computing, real numbers cannot be faithfully represented and differential equations can only be solved numerically with approximate algorithms (like the method of Euler or Runge–Kutta) using some form of discretization. Consequently, digital computers cannot run truly continuous simulations. Only analog computers can run truly continuous simulations.