System

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### System

##### Description

The System concept models the algorithmic implementation of the rhs. of the ODE x' = f(x,t). The only requirement for this concept is that it should be callable with a specific parameter syntax (see below). A System is typically implemented as a function or a functor. Systems fulfilling this concept are required by all Runge-Kutta steppers as well as the Bulirsch-Stoer steppers. However, symplectic and implicit steppers work with other system concepts, see Symplectic System and Implicit System.

##### Notation

`System`

  A type that is a model of System

`State`

  A type representing the state x of the ODE

`Deriv`

  A type representing the derivative x' of the ODE

`Time`

  A type representing the time

`sys`

  An object of type `System`

`x`

  Object of type `State`

`dxdt`

  Object of type `Deriv`

`t`

  Object of type `Time`

##### Valid expressions

Name | Expression | Type | Semantics
--- | --- | --- | ---
Calculate dx/dt := f(x,t) | `sys( x , dxdt , t )` | `void` | Calculates f(x,t), the result is stored into dxdt