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## Class template symplectic_rkn_sb3a_mclachlan

boost::numeric::odeint::symplectic_rkn_sb3a_mclachlan — Implement of the symmetric B3A method of Runge-Kutta-Nystroem method of sixth order.

## Synopsis

    // In header: <boost/numeric/odeint/stepper/symplectic_rkn_sb3a_mclachlan.hpp>

    template<typename Coor, typename Momentum = Coor, typename Value = double,
             typename CoorDeriv = Coor, typename MomentumDeriv = Coor,
             typename Time = Value,
             typename Algebra = typename algebra_dispatcher< Coor >::algebra_type,
             typename Operations = typename operations_dispatcher< Coor >::operations_type,
             typename Resizer = initially_resizer>
    class symplectic_rkn_sb3a_mclachlan : public symplectic_nystroem_stepper_base {
    public:
      // types
      typedef stepper_base_type::algebra_type algebra_type;
      typedef stepper_base_type::value_type   value_type;

      // construct/copy/destruct
      symplectic_rkn_sb3a_mclachlan(const algebra_type & = algebra_type());
    };

## Description

The method is of fourth order and has six stages. It is described HERE. This method cannot be used with multiprecision types since the coefficients are not defined analytically.

ToDo Add reference to the paper.

### Template Parameters

1.     typename Coor

   The type representing the coordinates q.

2.     typename Momentum = Coor

   The type representing the coordinates p.

3.     typename Value = double

   The basic value type. Should be something like float, double or a high-precision type.

4.     typename CoorDeriv = Coor

   The type representing the time derivative of the coordinate dq/dt.

5.     typename MomentumDeriv = Coor

6.     typename Time = Value

   The type representing the time t.

7.     typename Algebra = typename algebra_dispatcher< Coor >::algebra_type

   The algebra.

8.     typename Operations = typename operations_dispatcher< Coor >::operations_type

   The operations.

9.     typename Resizer = initially_resizer

   The resizer policy.

### `symplectic_rkn_sb3a_mclachlan` public construct/copy/destruct

1.     symplectic_rkn_sb3a_mclachlan(const algebra_type & algebra = algebra_type());

   Constructs the `symplectic_rkn_sb3a_mclachlan`. 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.