namespace boost {
  namespace numeric {
    namespace odeint {
      template<typename Stepper, typename System, typename State, 
               typename Time, typename Observer> 
        size_t integrate_adaptive(Stepper, System, State &, Time, Time, Time, 
                                  Observer);

      // Second version to solve the forwarding problem, can be called with Boost.Range as start_state. 
      template<typename Stepper, typename System, typename State, 
               typename Time, typename Observer> 
        size_t integrate_adaptive(Stepper stepper, System system, 
                                  const State & start_state, Time start_time, 
                                  Time end_time, Time dt, Observer observer);

      // integrate_adaptive without an observer. 
      template<typename Stepper, typename System, typename State, 
               typename Time> 
        size_t integrate_adaptive(Stepper stepper, System system, 
                                  State & start_state, Time start_time, 
                                  Time end_time, Time dt);

      // Second version to solve the forwarding problem, can be called with Boost.Range as start_state. 
      template<typename Stepper, typename System, typename State, 
               typename Time> 
        size_t integrate_adaptive(Stepper stepper, System system, 
                                  const State & start_state, Time start_time, 
                                  Time end_time, Time dt);
    }
  }
}