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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 = typename algebra_dispatcher< State >::algebra_type, 
         typename Operations = typename operations_dispatcher< State >::operations_type, 
         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 &);
};

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 = typename algebra_dispatcher< State >::algebra_type

    The algebra type.

  6. typename Operations = typename operations_dispatcher< State >::operations_type

    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.


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