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## Class template runge_kutta4_classic

boost::numeric::odeint::runge_kutta4_classic — The classical Runge-Kutta stepper of fourth order.

## Synopsis

    // In header: <boost/numeric/odeint/stepper/runge_kutta4_classic.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_kutta4_classic : public boost::numeric::odeint::explicit_stepper_base< Stepper, Order, State, Value, Deriv, Time, Algebra, Operations, Resizer >
    {
    public:
      // types
      typedef explicit_stepper_base< runge_kutta4_classic< ... >,... > stepper_base_type;
      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_type;

      // construct/copy/destruct
      runge_kutta4_classic(const algebra_type & = algebra_type());

      // public member functions
      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 StateType> void adjust_size(const StateType &);
      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>
        void do_step(System, const StateIn &, time_type, StateOut &, time_type);
      template<typename System, typename StateIn, typename DerivIn,
               typename StateOut>
        void do_step(System, const StateIn &, const DerivIn &, time_type,
                     StateOut &, time_type);
      template<typename StateIn> void adjust_size(const StateIn &);
      const algebra_type & algebra() const;

      // private member functions
      template<typename StateIn> bool resize_impl(const StateIn &);
    };

## Description

The Runge-Kutta method of fourth order is one standard method for solving ordinary differential equations and is widely used, see also en.wikipedia.org/wiki/Runge-Kutta_methods The method is explicit and fulfills the Stepper concept. Step size control or continuous output are not provided. This class implements the method directly, hence the generic Runge-Kutta algorithm is not used.

This class derives from explicit_stepper_base and inherits its interface via CRTP (current recurring template pattern). For more details see explicit_stepper_base.

### 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_kutta4_classic` public construct/copy/destruct

1.     runge_kutta4_classic(const algebra_type & algebra = algebra_type());

   Constructs the `runge_kutta4_classic` 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_kutta4_classic` public member functions

1.     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.

2.     template<typename StateType> void adjust_size(const StateType & 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.

3.     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.

4.     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.

5.     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. 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
   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.

6.     template<typename System, typename StateIn, typename StateOut>
         void do_step(System system, const StateIn & in, time_type t, StateOut & out,
                      time_type dt);

   The method performs one step. The state of the ODE is updated out-of-place.

   | 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.

7.     template<typename System, typename StateIn, typename DerivIn,
                typename StateOut>
         void do_step(System system, const StateIn & in, const DerivIn & dxdt,
                      time_type t, StateOut & out, time_type dt);

   The method performs one step. 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 );
       *

   | 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.

8.     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.

9.     const algebra_type & algebra() const;

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

### `runge_kutta4_classic` private member functions

1.     template<typename StateIn> bool resize_impl(const StateIn & x);