Continuous simulation
In continuous simulation, the smooth continuous response of a physical system is modeled by using ODEs . Newton's 2nd law, F=ma, is a good example of a single ODE continuous system. Numerical integration methods such as [Runge_kutta], or Bulirsch-Stoer are used to solve the system of ODEs. By coupling the ODE solver with other numerical operators and methods a continuous simulator can be used to model many different physical phenomena such as flight dynamics, robotics, automotive suspensions, hydraulics, electric power, electric motors, human respiration, polar ice cap melting, steam power plants etc. There is virtually no limit to the kinds of physical phenomena that can be modeled by a system of ODE's. Some systems though can not have all derivative terms specified explicitly from known inputs and other ODE outputs. Those derivative terms are defined implicitly by other system constraints such as Kirchoff's law that flow of current into a junction must equal flow out. To solve these implicit ODE systems a converging iterative scheme such as Newton-Raphson must be employed.