Error Stepper

This concepts specifies the interface an error stepper has to fulfill to be used within a ControlledErrorStepper. An error stepper must always fulfill the stepper concept. This can trivially implemented by

template< class System >
error_stepper::do_step( System sys , state_type &x , time_type t , time_type dt )
{
    state_type xerr;
    // allocate xerr
    do_step( sys , x , t , dt , xerr );
}

Description

An error stepper following this Error Stepper concept is capable of doing one step of the solution x(t) of an ODE with step-size dt to obtain x(t+dt) and also computing an error estimate x_err of the result. Error Steppers can be Runge-Kutta steppers, symplectic steppers as well as implicit steppers. Based on the stepper type, the ODE is defined as System, Symplectic System, Simple Symplectic System or Implicit System.

Refinement of

DefaultConstructable
CopyConstructable
Stepper

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 >.
order_type

Stepper::order_type

The type characterizing the order of the ODE, typically unsigned short.
stepper_category

Stepper::stepper_category

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

Notation

ErrorStepper: A type that is a model of Error Stepper
State: A type representing the state x of the ODE
Error: A type representing the error calculated by the stepper, usually same as State
Time: A type representing the time t of the ODE
stepper: An object of type ErrorStepper
x: Object of type State
xerr: Object of type Error
t, dt: Objects of type Time
sys: An object defining the ODE, should be a model of either System, Symplectic System, Simple Symplectic System or Implicit System.

Valid Expressions

Name	Expression	Type	Semantics
Get the stepper order	`stepper.order()`	`order_type`	Returns the order of the stepper for one step without error estimation.
Get the stepper order	`stepper.stepper_order()`	`order_type`	Returns the order of the stepper for one error estimation step which is used for error calculation.
Get the error order	`stepper.errorr_order()`	`order_type`	Returns the order of the error step which is used for error calculation.
Do step	`stepper.do_step( sys , x , t , dt )`	`void`	Performs one step of step size `dt`. The newly obtained state is written in-place to `x`.
Do step with error estimation	`stepper.do_step( sys , x , t , dt , xerr )`	`void`	Performs one step of step size `dt` with error estimation. The newly obtained state is written in-place to `x` and the estimated error to `xerr`.

Models

runge_kutta_cash_karp54
runge_kutta_dopri5
runge_kutta_fehlberg78
rosenbrock4