Controlled Stepper

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

A controlled stepper following this Controlled Stepper concept provides the possibility to perform one step of the solution x(t) of an ODE with step-size dt to obtain x(t+dt) with a given step-size dt. Depending on an error estimate of the solution the step might be rejected and a smaller step-size is suggested.

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 controlled_stepper_tag.

Notation

ControlledStepper: A type that is a model of Controlled Stepper
State: A type representing the state x of the ODE
Time: A type representing the time t of the ODE
stepper: An object of type ControlledStepper
x: Object of type State
t, dt: Objects of type Time
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
Do step	stepper.try_step( sys , x , t , dt )	`controlled_step_result`	Tries one step of step size `dt`. If the step was successful, `success` is returned, the resulting state is written to `x`, the new time is stored in `t` and `dt` now contains a new (possibly larger) step-size for the next step. If the error was too big, `rejected` is returned and the results are neglected - `x` and `t` are unchanged and `dt` now contains a reduced step-size to be used for the next try.

Name

Expression

Type

Semantics

Do step

stepper.try_step( sys , x , t , dt )

controlled_step_result

Tries one step of step size dt. If the step was successful, success is returned, the resulting state is written to x, the new time is stored in t and dt now contains a new (possibly larger) step-size for the next step. If the error was too big, rejected is returned and the results are neglected - x and t are unchanged and dt now contains a reduced step-size to be used for the next try.

Models

controlled_error_stepper< runge_kutta_cash_karp54 >
controlled_error_stepper_fsal< runge_kutta_dopri5 >
controlled_error_stepper< runge_kutta_fehlberg78 >
rosenbrock4_controller
bulirsch_stoer

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