Sandals::BVP< Real, N, M > Class Template Reference

Class container for an boundary value problem (BVP) of ODEs/DAEs. More...

#include <BVP.hh>

Public Types
using	VectorF = typename Implicit<Real, N, M>::VectorF
using	Pointer = std::shared_ptr<Implicit<Real, N, M>>
using	NewtonB = Optimist::RootFinder::Newton<Real, N>

Public Member Functions
	BVP (std::string t_name)
RungeKutta< Real, N, M > &	rk ()
RungeKutta< Real, N, M > const &	rk () const
virtual VectorF	b (VectorF const &x_ini, VectorF const &x_end) const =0
virtual MatrixJF	Jb_x_ini (VectorF const &x_ini, VectorF const &x_end) const =0
virtual MatrixJF	Jb_x_end (VectorF const &x_ini, VectorF const &x_end) const =0
bool	solve_single_shooting (VectorX const &t_mesh, VectorN const &ics, Solution< Real, N, M > &sol) const

Private Attributes
NewtonB	m_newton
RungeKutta< Real, N, M >	m_rk
std::string	m_name

Detailed Description

template<typename Real, Integer N, Integer M = 0>
class Sandals::BVP< Real, N, M >

Class container for an boundary value problem (BVP) of ordinary differential equations (ODEs) or differential algebraic equations (DAEs).

Template Parameters

Real	The scalar number type.
N	The dimension of the implicit ODE/DAE system.
M	The dimension of the invariants manifold.

Member Typedef Documentation

NewtonB

template<typename Real, Integer N, Integer M = 0>

using Sandals::BVP< Real, N, M >::NewtonB = Optimist::RootFinder::Newton<Real, N>

Templetized Newton solver for the boundary conditions.

Pointer

template<typename Real, Integer N, Integer M = 0>

using Sandals::BVP< Real, N, M >::Pointer = std::shared_ptr<Implicit<Real, N, M>>

Shared pointer to an implicit ODE system.

VectorF

template<typename Real, Integer N, Integer M = 0>

using Sandals::BVP< Real, N, M >::VectorF = typename Implicit<Real, N, M>::VectorF

Templetized vector type.

Constructor & Destructor Documentation

BVP()

template<typename Real, Integer N, Integer M = 0>

Sandals::BVP< Real, N, M >::BVP ( std::string t_name )

inline

Class constructor for the boundary value problem (BVP).

Parameters

[in]

t_name

The name of the BVP

Member Function Documentation

b()

template<typename Real, Integer N, Integer M = 0>

virtual VectorF Sandals::BVP< Real, N, M >::b ( VectorF const & x_ini, VectorF const & x_end ) const

pure virtual

Evaluate the boundary conditions function of the problem \( \mathbf{b}(\mathbf{x}_{\text{ini}}, \mathbf{x}_{\text{end}}) \).

Parameters

[in]	x_ini	Initial states \( \mathbf{x}_{\text{ini}} \).
[in]	x_end	Final states \( \mathbf{x}_{\text{end}} \).

Returns

The residual of the boundary conditions.

Jb_x_end()

template<typename Real, Integer N, Integer M = 0>

virtual MatrixJF Sandals::BVP< Real, N, M >::Jb_x_end ( VectorF const & x_ini, VectorF const & x_end ) const

pure virtual

Evaluate the Jacobian of the boundary conditions function \( \mathbf{b}(\mathbf{x}_{\text{ini}}, \mathbf{x}_{\text{end}}) \) with respect to the final states \( \mathbf{x}_{\text{end}} \).

Parameters

[in]	x_ini	Initial states \( \mathbf{x}_{\text{ini}} \).
[in]	x_end	Final states \( \mathbf{x}_{\text{end}} \).

Returns

The Jacobian \( \mathbf{Jb}_{\mathbf{x}_{\text{end}}}(\mathbf{x}_{\text{ini}}, \mathbf{x}_{\text{end}}) \).

Jb_x_ini()

template<typename Real, Integer N, Integer M = 0>

virtual MatrixJF Sandals::BVP< Real, N, M >::Jb_x_ini ( VectorF const & x_ini, VectorF const & x_end ) const

pure virtual

Evaluate the Jacobian of the boundary conditions function \( \mathbf{b}(\mathbf{x}_{\text{ini}}, \mathbf{x}_{\text{end}}) \) with respect to the initial states \( \mathbf{x}_{\text{ini}} \).

Parameters

[in]	x_ini	Initial states \( \mathbf{x}_{\text{ini}} \).
[in]	x_end	Final states \( \mathbf{x}_{\text{end}} \).

Returns

The Jacobian \( \mathbf{Jb}_{\mathbf{x}_{\text{ini}}}(\mathbf{x}_{\text{ini}}, \mathbf{x}_{\text{end}}) \).

rk() [1/2]

template<typename Real, Integer N, Integer M = 0>

RungeKutta< Real, N, M > & Sandals::BVP< Real, N, M >::rk ( )

inline

Get the Runge-Kutta method reference.

Returns

The Runge-Kutta method reference.

rk() [2/2]

template<typename Real, Integer N, Integer M = 0>

RungeKutta< Real, N, M > const & Sandals::BVP< Real, N, M >::rk ( ) const

inline

Get the Runge-Kutta method const reference.

Returns

The Runge-Kutta method const reference.

solve_single_shooting()

template<typename Real, Integer N, Integer M = 0>

bool Sandals::BVP< Real, N, M >::solve_single_shooting ( VectorX const & t_mesh, VectorN const & ics, Solution< Real, N, M > & sol ) const

inline

Solve the boundary value problem (BVP) using the Runge-Kutta method uning a single shooting method.

Parameters

[in]	t_mesh	Independent variable (or time) mesh \( \mathbf{t} \).
[in]	ics	Initial conditions \( \mathbf{x}(t = 0) \).
[out]	sol	The solution of the system over the mesh of independent variable.

Returns

True if the system is successfully solved, false otherwise.

Warning

Do not use the solution for internal backtracking, as the step callback may directly modify the solution.

Member Data Documentation

m_name

template<typename Real, Integer N, Integer M = 0>

std::string Sandals::BVP< Real, N, M >::m_name

private

Name of the ODE/DAE system.

m_newton

template<typename Real, Integer N, Integer M = 0>

NewtonB Sandals::BVP< Real, N, M >::m_newton

mutableprivate

Newton solver for the boundary conditions.

m_rk

template<typename Real, Integer N, Integer M = 0>

RungeKutta<Real, N, M> Sandals::BVP< Real, N, M >::m_rk

private

Runge-Kutta method for the BVP.

---

The documentation for this class was generated from the following file:

• include/Sandals/BVP.hh