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boost::numeric::odeint::runge_kutta_dopri5 — The RungeKutta DormandPrince 5 method.
// In header: <boost/numeric/odeint/stepper/runge_kutta_dopri5.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_dopri5 : public explicit_error_stepper_fsal_base { public: // types typedef explicit_error_stepper_fsal_base< runge_kutta_dopri5< ... >,... > 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; // public member functions runge_kutta_dopri5(const algebra_type & = algebra_type()); template<typename System, typename StateIn, typename DerivIn, typename StateOut, typename DerivOut> void do_step_impl(System, const StateIn &, const DerivIn &, time_type, StateOut &, DerivOut &, time_type); template<typename System, typename StateIn, typename DerivIn, typename StateOut, typename DerivOut, typename Err> void do_step_impl(System, const StateIn &, const DerivIn &, time_type, StateOut &, DerivOut &, time_type, Err &); template<typename StateOut, typename StateIn1, typename DerivIn1, typename StateIn2, typename DerivIn2> void calc_state(time_type, StateOut &, const StateIn1 &, const DerivIn1 &, time_type, const StateIn2 &, const DerivIn2 &, time_type) const; template<typename StateIn> void adjust_size(const StateIn &); // private member functions template<typename StateIn> bool resize_k_x_tmp_impl(const StateIn &); template<typename StateIn> bool resize_dxdt_tmp_impl(const StateIn &); };
The RungeKutta DormandPrince 5 method is a very popular method for solving ODEs, see . The method is explicit and fulfills the Error Stepper concept. Step size control is provided but continuous output is available which make this method favourable for many applications.
This class derives from explicit_error_stepper_fsal_base and inherits its interface via CRTP (current recurring template pattern). The method possesses the FSAL (firstsameaslast) property. See explicit_error_stepper_fsal_base for more details.
typename State
The state type.
typename Value = double
The value type.
typename Deriv = State
The type representing the time derivative of the state.
typename Time = Value
The time representing the independent variable  the time.
typename Algebra = typename algebra_dispatcher< State >::algebra_type
The algebra type.
typename Operations = typename operations_dispatcher< State >::operations_type
The operations type.
typename Resizer = initially_resizer
The resizer policy type.
runge_kutta_dopri5
public member functionsrunge_kutta_dopri5(const algebra_type & algebra = algebra_type());Constructs the runge_kutta_dopri5 class. This constructor can be used as a default constructor if the algebra has a default constructor.
Parameters: 

template<typename System, typename StateIn, typename DerivIn, typename StateOut, typename DerivOut> void do_step_impl(System system, const StateIn & in, const DerivIn & dxdt_in, time_type t, StateOut & out, DerivOut & dxdt_out, time_type dt);This method performs one step. The derivative
dxdt_in
of in
at the time t
is passed to the method. The result is updated outofplace, hence the input is in in
and the output in out
. Furthermore, the derivative is update outofplace, hence the input is assumed to be in dxdt_in
and the output in dxdt_out
. Access to this step functionality is provided by explicit_error_stepper_fsal_base and do_step_impl
should not be called directly.
Parameters: 

template<typename System, typename StateIn, typename DerivIn, typename StateOut, typename DerivOut, typename Err> void do_step_impl(System system, const StateIn & in, const DerivIn & dxdt_in, time_type t, StateOut & out, DerivOut & dxdt_out, time_type dt, Err & xerr);This method performs one step. The derivative
dxdt_in
of in
at the time t
is passed to the method. The result is updated outofplace, hence the input is in in
and the output in out
. Furthermore, the derivative is update outofplace, hence the input is assumed to be in dxdt_in
and the output in dxdt_out
. Access to this step functionality is provided by explicit_error_stepper_fsal_base and do_step_impl
should not be called directly. An estimation of the error is calculated.
Parameters: 

template<typename StateOut, typename StateIn1, typename DerivIn1, typename StateIn2, typename DerivIn2> void calc_state(time_type t, StateOut & x, const StateIn1 & x_old, const DerivIn1 & deriv_old, time_type t_old, const StateIn2 &, const DerivIn2 & deriv_new, time_type t_new) const;This method is used for continuous output and it calculates the state
x
at a time t
from the knowledge of two states old_state
and current_state
at time points t_old
and t_new
. It also uses internal variables to calculate the result. Hence this method must be called after two successful do_step
calls. template<typename StateIn> void adjust_size(const StateIn & x);Adjust the size of all temporaries in the stepper manually.
Parameters: 
