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// G4HelixImplicitEuler
//
// Class description:
//
//  Helix Implicit Euler stepper for magnetic field:
//        x_1 = x_0 + 1/2 * ( helix(h,t_0,x_0)
//                          + helix(h,t_0+h,x_0+helix(h,t0,x0) ) )
//  Second order solver.
//  Take the current derivative and add it to the current position.
//  Take the output and its derivative. Add the mean of both derivatives
//  to form the final output.

// Author: W.Wander (MIT), 03.11.1998
// -------------------------------------------------------------------
#ifndef G4HELIXIMPLICITEULER_HH
#define G4HELIXIMPLICITEULER_HH

#include "G4MagHelicalStepper.hh"

/**
 * @brief G4HelixImplicitEuler implements a helix implicit Euler
 * stepper for magnetic field with 2nd order solver.
 */

class G4HelixImplicitEuler : public G4MagHelicalStepper
{
  public:

    /**
     * Constructor for G4HelixImplicitEuler.
     *  @param[in] EqRhs Pointer to the provided equation of motion.
     */
    G4HelixImplicitEuler(G4Mag_EqRhs* EqRhs);

    /**
     * Default Destructor.
     */
    ~G4HelixImplicitEuler() override = default;
  
    /**
     * The stepper function for the integration.
     *  @param[in] y Starting values array of integration variables.
     *  @param[in] Bfld Derivatives array.
     *  @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, "kHelixImplicitEuler".
     */
    inline G4StepperType StepperType() const override { return kHelixImplicitEuler; }
};

#endif
