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+[/============================================================================
+ Boost.odeint
+
+ Copyright (c) 2009-2013 Karsten Ahnert
+ Copyright (c) 2009-2013 Mario Mulansky
+
+ 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 Dense Output Stepper]
+
+This concept specifies the interface a dense output stepper has to fulfill to be used within __integrate_functions.
+
+[heading Description]
+A dense output stepper following this Dense Output Stepper concept provides the possibility to perform a single step of the solution /x(t)/ of an ODE to obtain /x(t+dt)/.
+The step-size `dt` might be adjusted automatically due to error control.
+Dense output steppers also can interpolate the solution to calculate the state /x(t')/ at any point /t <= t' <= t+dt/.
+
+[heading Associated types]
+
+* '''<para>'''[*state_type]'''</para>'''
+'''<para>'''`Stepper::state_type`'''</para>'''
+'''<para>'''The type characterizing the state of the ODE, hence ['x].'''</para>'''
+
+* '''<para>'''[*deriv_type]'''</para>'''
+'''<para>'''`Stepper::deriv_type`'''</para>'''
+'''<para>'''The type characterizing the derivative of the ODE, hence ['d x/dt].'''</para>'''
+
+* '''<para>'''[*time_type]'''</para>'''
+'''<para>'''`Stepper::time_type`'''</para>'''
+'''<para>'''The type characterizing the dependent variable of the ODE, hence the time ['t].'''</para>'''
+
+* '''<para>'''[*value_type]'''</para>'''
+'''<para>'''`Stepper::value_type`'''</para>'''
+'''<para>'''The numerical data type which is used within the stepper, something like `float`, `double`, `complex< double >`.'''</para>'''
+
+* '''<para>'''[*stepper_category]'''</para>'''
+'''<para>'''`Stepper::stepper_category`'''</para>'''
+'''<para>'''A tag type characterizing the category of the stepper. This type must be convertible to `dense_output_stepper_tag`.'''</para>'''
+
+
+[heading Notation]
+
+[variablelist
+ [[`Stepper`] [A type that is a model of Dense Output Stepper]]
+ [[`State`] [A type representing the state /x/ of the ODE]]
+ [[`stepper`] [An object of type `Stepper`]]
+ [[`x0`, `x`] [Object of type `State`]]
+ [[`t0`, `dt0`, `t`] [Objects of type `Stepper::time_type`]]
+ [[`sys`] [An object defining the ODE, should be a model of __system, __symplectic_system, __simple_symplectic_system or __implicit_system.]]
+]
+
+[heading Valid Expressions]
+
+[table
+ [[Name] [Expression] [Type] [Semantics]]
+
+ [[Initialize integration] [`stepper.initialize( x0 , t0 , dt0 )`] [void] [Initializes the stepper with initial values `x0`, `t0` and `dt0`.]]
+
+ [[Do step] [`stepper.do_step( sys )`] [`std::pair< Stepper::time_type , Stepper::time_type >`] [Performs one step using the ODE defined by `sys`. The step-size might be changed internally due to error control. This function returns a pair containing `t` and `t+dt` representing the interval for which interpolation can be performed.] ]
+
+ [/ [Do step with reference] [`stepper.do_step( boost::ref( sys ) )`] [`std::pair< Stepper::time_type , Stepper::time_type >`] [Same as above with `System` as reference] ]
+
+ [[Do interpolation] [`stepper.calc_state( t_inter , x )`] [`void`] [Performs the interpolation to calculate /x(t[sub inter]/) where /t <= t[sub inter] <= t+dt/.]]
+
+ [[Get current time] [`stepper.current_time()`] [`const Stepper::time_type&`] [Returns the current time /t+dt/ of the stepper, that is the end time of the last step and the starting time for the next call of `do_step`]]
+
+ [[Get current state] [`stepper.current_state()`] [`const Stepper::state_type&`] [Returns the current state of the stepper, that is /x(t+dt)/, the state at the time returned by `stepper.current_time()`]]
+
+ [[Get current time step] [`stepper.current_time_step()`] [`const
+ Stepper::time_type&`] [Returns the current step size of the stepper, that is
+ /dt/]]
+]
+
+[heading Models]
+
+* `dense_output_controlled_explicit_fsal< controlled_error_stepper_fsal< runge_kutta_dopri5 >`
+* `bulirsch_stoer_dense_out`
+* `rosenbrock4_dense_output`
+
+[endsect]