Stepper

This concepts specifies the interface a simple stepper has to fulfill to be used within the integrate functions.

The basic stepper concept. A basic stepper following this Stepper concept is able to perform a single step of the solution x(t) of an ODE to obtain x(t+dt) using a given step size dt. Basic steppers can be Runge-Kutta steppers, symplectic steppers as well as implicit steppers. Depending on the actual stepper, the ODE is defined as System, Symplectic System, Simple Symplectic System or Implicit System. Note that all error steppers are also basic steppers.

Refinement of

DefaultConstructable
CopyConstructable

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 stepper_tag.

Notation

Stepper: A type that is a model of 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 Stepper
x: Object of type State
t, dt: Objects of type Time
sys: An object defining the ODE. Depending on the Stepper this might be a model of System, Symplectic System, Simple Symplectic System or Implicit System

Valid Expressions

Name	Expression	Type	Semantics
Get the order	`stepper.order()`	`order_type`	Returns the order of the stepper.
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 in `x`.

Models

runge_kutta4
euler
runge_kutta_cash_karp54
runge_kutta_dopri5
runge_kutta_fehlberg78
modified_midpoint
rosenbrock4

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