Dense Output Stepper

This concept specifies the interface a dense output stepper has to fulfill to be used within integrate functions.

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.

Associated types

state_type

Stepper::state_type

The type characterizing the state of the ODE, hence x.
deriv_type

Stepper::deriv_type

The type characterizing the derivative of the ODE, hence d x/dt.
time_type

Stepper::time_type

The type characterizing the dependent variable of the ODE, hence the time t.
value_type

Stepper::value_type

The numerical data type which is used within the stepper, something like float, double, complex< double >.
stepper_category

Stepper::stepper_category

A tag type characterizing the category of the stepper. This type must be convertible to dense_output_stepper_tag.

Notation

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.

Valid Expressions

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 interpolation	`stepper.calc_state( t_inter , x )`	`void`	Performs the interpolation to calculate /x(t_inter/) where /t <= t_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

Models

dense_output_controlled_explicit_fsal< controlled_error_stepper_fsal< runge_kutta_dopri5 >
bulirsch_stoer_dense_out
rosenbrock4_dense_output

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