[ceph.git] / ceph / src / boost / libs / numeric / odeint / doc / concepts / system.qbk

[/============================================================================
  Boost.odeint

  Copyright 2011 Mario Mulansky
  Copyright 2011-2012 Karsten Ahnert

  Use, modification and distribution is subject to the Boost Software License,
  Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
  http://www.boost.org/LICENSE_1_0.txt)
=============================================================================/]


[section System]

[heading 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.

[heading Notation]

[variablelist
  [[`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`]]
]

[heading Valid expressions]

[table
  [[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] ]
]

[endsect]
Commit	Line	Data
7c673cae FG	1	[/============================================================================
	2	Boost.odeint
	3
	4	Copyright 2011 Mario Mulansky
	5	Copyright 2011-2012 Karsten Ahnert
	6
	7	Use, modification and distribution is subject to the Boost Software License,
	8	Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
	9	http://www.boost.org/LICENSE_1_0.txt)
	10	=============================================================================/]
	11
	12
	13	[section System]
	14
	15	[heading Description]
	16
	17	The System concept models the algorithmic implementation of the rhs. of the ODE ['x' = f(x,t)].
	18	The only requirement for this concept is that it should be callable with a specific parameter syntax (see below).
	19	A System is typically implemented as a function or a functor.
	20	Systems fulfilling this concept are required by all Runge-Kutta steppers as well as the Bulirsch-Stoer steppers.
	21	However, symplectic and implicit steppers work with other system concepts, see __symplectic_system and __implicit_system.
	22
	23	[heading Notation]
	24
	25	[variablelist
	26	[[`System`] [A type that is a model of System]]
	27	[[`State`] [A type representing the state /x/ of the ODE]]
	28	[[`Deriv`] [A type representing the derivative /x'/ of the ODE]]
	29	[[`Time`] [A type representing the time]]
	30	[[`sys`] [An object of type `System`]]
	31	[[`x`] [Object of type `State`]]
	32	[[`dxdt`] [Object of type `Deriv`]]
	33	[[`t`] [Object of type `Time`]]
	34	]
	35
	36	[heading Valid expressions]
	37
	38	[table
	39	[[Name] [Expression] [Type] [Semantics]]
	40	[[Calculate ['dx/dt := f(x,t)]] [`sys( x , dxdt , t )`] [`void`] [Calculates f(x,t), the result is stored into dxdt] ]
	41	]
	42
	43	[endsect]