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// G4HelixHeum
//
// Class description:
//
// Simple Heum stepper for magnetic field:
//     x_1 = x_0 +
//           h * 1/4 * dx(t0,x0)  +
//               3/4 * dx(t0+2/3*h, x0+2/3*h*(dx(t0+h/3,x0+h/3*dx(t0,x0)))) 
// Third order solver.

// Author: W.Wander (MIT), 03.11.1998
// -------------------------------------------------------------------
#ifndef G4HELIXHEUM_HH
#define G4HELIXHEUM_HH

#include "G4MagHelicalStepper.hh"

/**
 * @brief G4HelixHeum implements a simple Heum stepper for magnetic field
 * with 3rd order solver.
 */

class G4HelixHeum : public G4MagHelicalStepper
{
  public:

    /**
     * Constructor for G4HelixHeum.
     *  @param[in] EqRhs Pointer to the provided equation of motion.
     */
    G4HelixHeum(G4Mag_EqRhs* EqRhs);

    /**
     * Default Destructor.
     */
    ~G4HelixHeum() override = default;
  
    /**
     * The stepper function for the integration.
     *  @param[in] y Starting values array of integration variables.
     *  @param[in] Bfld The field vector.
     *  @param[in] h The given step size.
     *  @param[out] yout Integration output.
     */
    void DumbStepper( const G4double y[],
                            G4ThreeVector Bfld,
                            G4double h,
                            G4double yout[] ) override;

    /**
     * Returns the order, 2, of integration.
     */
    inline G4int IntegratorOrder() const override { return 2; }

    /**
     * Returns the stepper type-ID, "kHelixHeum".
     */
    inline G4StepperType StepperType() const override { return kHelixHeum; }
};

#endif