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Class template runge_kutta_cash_karp54

boost::numeric::odeint::runge_kutta_cash_karp54 — The Runge-Kutta Cash-Karp method.

Synopsis

// In header: <boost/numeric/odeint/stepper/runge_kutta_cash_karp54.hpp>

template<typename State, typename Value = double, typename Deriv = State, 
         typename Time = Value, typename Algebra = range_algebra, 
         typename Operations = default_operations, 
         typename Resizer = initially_resizer> 
class runge_kutta_cash_karp54 : public boost::numeric::odeint::explicit_error_generic_rk< StageCount, Order, StepperOrder, ErrorOrder, State, Value, Deriv, Time, Algebra, Operations, Resizer >
{
public:
  // types
  typedef stepper_base_type::state_type      state_type;     
  typedef stepper_base_type::value_type      value_type;     
  typedef stepper_base_type::deriv_type      deriv_type;     
  typedef stepper_base_type::time_type       time_type;      
  typedef stepper_base_type::algebra_type    algebra_type;   
  typedef stepper_base_type::operations_type operations_type;
  typedef stepper_base_type::resizer_type    resizer_typ;    

  // construct/copy/destruct
  runge_kutta_cash_karp54(const algebra_type & = algebra_type());

  // public member functions
  template<typename System, typename StateIn, typename DerivIn, 
           typename StateOut, typename Err> 
    void do_step_impl(System, const StateIn &, const DerivIn &, time_type, 
                      StateOut &, time_type, Err &);
  template<typename System, typename StateIn, typename DerivIn, 
           typename StateOut> 
    void do_step_impl(System, const StateIn &, const DerivIn &, time_type, 
                      StateOut &, time_type);
  template<typename StateIn> void adjust_size(const StateIn &);
  order_type order(void) const;
  order_type stepper_order(void) const;
  order_type error_order(void) const;
  template<typename System, typename StateInOut> 
    void do_step(System, StateInOut &, time_type, time_type);
  template<typename System, typename StateInOut> 
    void do_step(System, const StateInOut &, time_type, time_type);
  template<typename System, typename StateInOut, typename DerivIn> 
    boost::disable_if< boost::is_same< DerivIn, time_type >, void >::type 
    do_step(System, StateInOut &, const DerivIn &, time_type, time_type);
  template<typename System, typename StateIn, typename StateOut> 
    boost::disable_if< boost::is_same< StateIn, time_type >, void >::type 
    do_step(System, const StateIn &, time_type, StateOut &, time_type);
  template<typename System, typename StateIn, typename DerivIn, 
           typename StateOut> 
    boost::disable_if< boost::is_same< DerivIn, time_type >, void >::type 
    do_step(System, const StateIn &, const DerivIn &, time_type, StateOut &, 
            time_type);
  template<typename System, typename StateInOut, typename Err> 
    void do_step(System, StateInOut &, time_type, time_type, Err &);
  template<typename System, typename StateInOut, typename Err> 
    void do_step(System, const StateInOut &, time_type, time_type, Err &);
  template<typename System, typename StateInOut, typename DerivIn, 
           typename Err> 
    boost::disable_if< boost::is_same< DerivIn, time_type >, void >::type 
    do_step(System, StateInOut &, const DerivIn &, time_type, time_type, 
            Err &);
  template<typename System, typename StateIn, typename StateOut, typename Err> 
    void do_step(System, const StateIn &, time_type, StateOut &, time_type, 
                 Err &);
  template<typename System, typename StateIn, typename DerivIn, 
           typename StateOut, typename Err> 
    void do_step(System, const StateIn &, const DerivIn &, time_type, 
                 StateOut &, time_type, Err &);
  algebra_type & algebra();
  const algebra_type & algebra() const;
};

Description

The Runge-Kutta Cash-Karp method is one of the standard methods for solving ordinary differential equations, see en.wikipedia.org/wiki/Cash-Karp_methods. The method is explicit and fulfills the Error Stepper concept. Step size control is provided but continuous output is not available for this method.

This class derives from explicit_error_stepper_base and inherits its interface via CRTP (current recurring template pattern). Furthermore, it derivs from explicit_error_generic_rk which is a generic Runge-Kutta algorithm with error estimation. For more details see explicit_error_stepper_base and explicit_error_generic_rk.

Template Parameters

  1. typename State

    The state type.

  2. typename Value = double

    The value type.

  3. typename Deriv = State

    The type representing the time derivative of the state.

  4. typename Time = Value

    The time representing the independent variable - the time.

  5. typename Algebra = range_algebra

    The algebra type.

  6. typename Operations = default_operations

    The operations type.

  7. typename Resizer = initially_resizer

    The resizer policy type.

runge_kutta_cash_karp54 public construct/copy/destruct

  1. runge_kutta_cash_karp54(const algebra_type & algebra = algebra_type());
    Constructs the runge_kutta_cash_karp54 class. This constructor can be used as a default constructor if the algebra has a default constructor.

    Parameters:

    algebra

    A copy of algebra is made and stored inside explicit_stepper_base.

runge_kutta_cash_karp54 public member functions

  1. template<typename System, typename StateIn, typename DerivIn, 
             typename StateOut, typename Err> 
      void do_step_impl(System system, const StateIn & in, const DerivIn & dxdt, 
                        time_type t, StateOut & out, time_type dt, Err & xerr);
    This method performs one step. The derivative `dxdt` of `in` at the time `t` is passed to the method. The result is updated out-of-place, hence the input is in `in` and the output in `out`. Futhermore, an estimation of the error is stored in `xerr`. `do_step_impl` is used by explicit_error_stepper_base.

    Parameters:

    dt

    The step size.

    dxdt

    The derivative of x at t.

    in

    The state of the ODE which should be solved. in is not modified in this method

    out

    The result of the step is written in out.

    system

    The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept.

    t

    The value of the time, at which the step should be performed.

    xerr

    The result of the error estimation is written in xerr.

  2. template<typename System, typename StateIn, typename DerivIn, 
             typename StateOut> 
      void do_step_impl(System system, const StateIn & in, const DerivIn & dxdt, 
                        time_type t, StateOut & out, time_type dt);
    This method performs one step. The derivative `dxdt` of `in` at the time `t` is passed to the method. The result is updated out-of-place, hence the input is in `in` and the output in `out`. Access to this step functionality is provided by explicit_stepper_base and `do_step_impl` should not be called directly.

    Parameters:

    dt

    The step size.

    dxdt

    The derivative of x at t.

    in

    The state of the ODE which should be solved. in is not modified in this method

    out

    The result of the step is written in out.

    system

    The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept.

    t

    The value of the time, at which the step should be performed.

  3. template<typename StateIn> void adjust_size(const StateIn & x);
    Adjust the size of all temporaries in the stepper manually.

    Parameters:

    x

    A state from which the size of the temporaries to be resized is deduced.

  4. order_type order(void) const;

    Returns:

    Returns the order of the stepper if it used without error estimation.

  5. order_type stepper_order(void) const;

    Returns:

    Returns the order of a step if the stepper is used without error estimation.

  6. order_type error_order(void) const;

    Returns:

    Returns the order of an error step if the stepper is used without error estimation.

  7. template<typename System, typename StateInOut> 
      void do_step(System system, StateInOut & x, time_type t, time_type dt);
    This method performs one step. It transforms the result in-place.

    Parameters:

    dt

    The step size.

    system

    The system function to solve, hence the r.h.s. of the ordinary differential equation. It must fulfill the Simple System concept.

    t

    The value of the time, at which the step should be performed.

    x

    The state of the ODE which should be solved. After calling do_step the result is updated in x.

  8. template<typename System, typename StateInOut> 
      void do_step(System system, const StateInOut & x, time_type t, time_type dt);
    Second version to solve the forwarding problem, can be called with Boost.Range as StateInOut.
  9. template<typename System, typename StateInOut, typename DerivIn> 
      boost::disable_if< boost::is_same< DerivIn, time_type >, void >::type 
      do_step(System system, StateInOut & x, const DerivIn & dxdt, time_type t, 
              time_type dt);
    The method performs one step with the stepper passed by Stepper. Additionally to the other method the derivative of x is also passed to this method. It is supposed to be used in the following way:
     sys( x , dxdt , t );
     stepper.do_step( sys , x , dxdt , t , dt );
    

    The result is updated in place in x. This method is disabled if Time and Deriv are of the same type. In this case the method could not be distinguished from other `do_step` versions.

    [Note] Note

    This method does not solve the forwarding problem.

    Parameters:

    dt

    The step size.

    dxdt

    The derivative of x at t.

    system

    The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept.

    t

    The value of the time, at which the step should be performed.

    x

    The state of the ODE which should be solved. After calling do_step the result is updated in x.

  10. template<typename System, typename StateIn, typename StateOut> 
      boost::disable_if< boost::is_same< StateIn, time_type >, void >::type 
      do_step(System system, const StateIn & in, time_type t, StateOut & out, 
              time_type dt);
    The method performs one step with the stepper passed by Stepper. The state of the ODE is updated out-of-place. This method is disabled if StateIn and Time are the same type. In this case the method can not be distinguished from other `do_step` variants.
    [Note] Note

    This method does not solve the forwarding problem.

    Parameters:

    dt

    The step size.

    in

    The state of the ODE which should be solved. in is not modified in this method

    out

    The result of the step is written in out.

    system

    The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept.

    t

    The value of the time, at which the step should be performed.

  11. template<typename System, typename StateIn, typename DerivIn, 
             typename StateOut> 
      boost::disable_if< boost::is_same< DerivIn, time_type >, void >::type 
      do_step(System system, const StateIn & in, const DerivIn & dxdt, 
              time_type t, StateOut & out, time_type dt);
    The method performs one step with the stepper passed by Stepper. The state of the ODE is updated out-of-place. Furthermore, the derivative of x at t is passed to the stepper. It is supposed to be used in the following way:
     sys( in , dxdt , t );
     stepper.do_step( sys , in , dxdt , t , out , dt );
    

    This method is disabled if DerivIn and Time are of same type.

    [Note] Note

    This method does not solve the forwarding problem.

    Parameters:

    dt

    The step size.

    dxdt

    The derivative of x at t.

    in

    The state of the ODE which should be solved. in is not modified in this method

    out

    The result of the step is written in out.

    system

    The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept.

    t

    The value of the time, at which the step should be performed.

  12. template<typename System, typename StateInOut, typename Err> 
      void do_step(System system, StateInOut & x, time_type t, time_type dt, 
                   Err & xerr);
    The method performs one step with the stepper passed by Stepper and estimates the error. The state of the ODE is updated in-place.

    Parameters:

    dt

    The step size.

    system

    The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept.

    t

    The value of the time, at which the step should be performed.

    x

    The state of the ODE which should be solved. x is updated by this method.

    xerr

    The estimation of the error is stored in xerr.

  13. template<typename System, typename StateInOut, typename Err> 
      void do_step(System system, const StateInOut & x, time_type t, time_type dt, 
                   Err & xerr);
    Second version to solve the forwarding problem, can be called with Boost.Range as StateInOut.
  14. template<typename System, typename StateInOut, typename DerivIn, typename Err> 
      boost::disable_if< boost::is_same< DerivIn, time_type >, void >::type 
      do_step(System system, StateInOut & x, const DerivIn & dxdt, time_type t, 
              time_type dt, Err & xerr);
    The method performs one step with the stepper passed by Stepper. Additionally to the other method the derivative of x is also passed to this method. It is supposed to be used in the following way:
     sys( x , dxdt , t );
     stepper.do_step( sys , x , dxdt , t , dt , xerr );
    

    The result is updated in place in x. This method is disabled if Time and DerivIn are of the same type. In this case the method could not be distinguished from other `do_step` versions.

    [Note] Note

    This method does not solve the forwarding problem.

    Parameters:

    dt

    The step size.

    dxdt

    The derivative of x at t.

    system

    The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept.

    t

    The value of the time, at which the step should be performed.

    x

    The state of the ODE which should be solved. After calling do_step the result is updated in x.

    xerr

    The error estimate is stored in xerr.

  15. template<typename System, typename StateIn, typename StateOut, typename Err> 
      void do_step(System system, const StateIn & in, time_type t, StateOut & out, 
                   time_type dt, Err & xerr);
    The method performs one step with the stepper passed by Stepper. The state of the ODE is updated out-of-place. Furthermore, the error is estimated.
    [Note] Note

    This method does not solve the forwarding problem.

    Parameters:

    dt

    The step size.

    in

    The state of the ODE which should be solved. in is not modified in this method

    out

    The result of the step is written in out.

    system

    The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept.

    t

    The value of the time, at which the step should be performed.

    xerr

    The error estimate.

  16. template<typename System, typename StateIn, typename DerivIn, 
             typename StateOut, typename Err> 
      void do_step(System system, const StateIn & in, const DerivIn & dxdt, 
                   time_type t, StateOut & out, time_type dt, Err & xerr);
    The method performs one step with the stepper passed by Stepper. The state of the ODE is updated out-of-place. Furthermore, the derivative of x at t is passed to the stepper and the error is estimated. It is supposed to be used in the following way:
     sys( in , dxdt , t );
     stepper.do_step( sys , in , dxdt , t , out , dt );
    

    This method is disabled if DerivIn and Time are of same type.

    [Note] Note

    This method does not solve the forwarding problem.

    Parameters:

    dt

    The step size.

    dxdt

    The derivative of x at t.

    in

    The state of the ODE which should be solved. in is not modified in this method

    out

    The result of the step is written in out.

    system

    The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept.

    t

    The value of the time, at which the step should be performed.

    xerr

    The error estimate.

  17. algebra_type & algebra();

    Returns:

    A reference to the algebra which is held by this class.

  18. const algebra_type & algebra() const;

    Returns:

    A const reference to the algebra which is held by this class.


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