Define the Berman equation by inheriting Equation base class. More...

Inheritance diagram for CppNoddy::Example::Berman_equation:

Public Member Functions
	Berman_equation ()
	Construct the Berman equation as a 4th order real system. More...

void	residual_fn (const DenseVector< double > &z, DenseVector< double > &f) const
	We implement the equation as 4 first-order ODEs. More...

void	mass (const DenseVector< double > &x, DenseMatrix< double > &m) const

	Berman_equation ()
	The Berman equation is a 4th order real ODE. More...

void	residual_fn (const DenseVector< double > &z, DenseVector< double > &g) const
	The Berman equation. More...

void	matrix0 (const DenseVector< double > &x, DenseMatrix< double > &m) const
	Define the matrix in terms of the current state vector. More...

Public Member Functions inherited from CppNoddy::Equation< double >
	Equation (const unsigned &order)
	Constructor for equation class. More...

virtual	~Equation ()
	An empty destructor, virtual since we have virtual methods. More...

Public Member Functions inherited from CppNoddy::Residual_with_coords< _Type, _Xtype >
	Residual_with_coords (const unsigned &order, const unsigned &ncoords)
	Constructor for a 'square' residual object that is, N residuals for N unknowns. More...

	Residual_with_coords (const unsigned &order, const unsigned &nvars, const unsigned &ncoords)
	Constructor for a 'non-square' residual object that is, there are less residual constraints than unknowns. More...

virtual	~Residual_with_coords ()
	An empty destructor. More...

_Xtype &	coord (const unsigned &i)
	General handle access to the coordinates. More...

const _Xtype &	coord (const unsigned &i) const
	General handle access to the coordinates. More...

Public Member Functions inherited from CppNoddy::Residual< _Type >
	Residual (const unsigned &order)
	Constructor for a 'square' residual object that is, N residuals for N unknowns. More...

	Residual (const unsigned &order, const unsigned &nvars)
	Constructor for a 'non-square' residual object that is, there are less residual constraints than unknowns. More...

virtual	~Residual ()
	An empty destructor, virtual since we have virtual methods. More...

void	update (const DenseVector< _Type > &state)
	Update the Residual object for the current set of state variables. More...

const DenseVector< _Type > &	residual () const
	Return a handle to the residuals corresponding to the last update state. More...

const DenseMatrix< _Type > &	jacobian () const
	Retrun a handle to the Jacobian of the residual corresponding to the last update state. More...

_Type &	delta ()

const _Type &	delta () const

unsigned	get_order () const
	Get the order of the residual vector. More...

unsigned	get_number_of_vars () const
	Get the number of variables that this residual condition is defined for. More...

virtual void	residual_fn (const DenseVector< _Type > &state, DenseVector< _Type > &f) const
	A blank virtual residual function method. More...

Public Member Functions inherited from CppNoddy::Equation_1matrix< double >
	Equation_1matrix (const unsigned &order)
	Constructor for equation class. More...

virtual	~Equation_1matrix ()
	An empty destructor, virtual since we have virtual methods. More...

void	update (const DenseVector< double > &state)
	Update the Equation object for the current set of state variables. More...

const DenseMatrix< double > &	matrix0 () const
	Return a handle to the matrix. More...

virtual void	get_jacobian_of_matrix0_mult_vector (const DenseVector< double > &state, const DenseVector< double > &vec, DenseMatrix< double > &h) const
	Return the product of the Jacobian-of-the-matrix and a vector 'vec' when the equation has a given 'state'. More...

Public Attributes
double	Re
	The Reynolds number. More...

Additional Inherited Members
Protected Member Functions inherited from CppNoddy::Residual< _Type >
virtual void	jacobian (const DenseVector< _Type > &state, DenseMatrix< _Type > &jac) const
	Because the residual evaluation at the current state is assumed to have already been done by the 'update' method, this routine is protected. More...

virtual void	matrix0 (const DenseVector< double > &x, DenseMatrix< double > &m) const
	Define the matrix in terms of the current state vector. More...

Protected Attributes inherited from CppNoddy::Residual_with_coords< _Type, _Xtype >
std::vector< _Xtype >	coords
	The coordinates stored for this residual. More...

Protected Attributes inherited from CppNoddy::Residual< _Type >
DenseMatrix< _Type >	JAC_AT_LAST_STATE
	Jacobian for the last state vector. More...

DenseVector< _Type >	FN_AT_LAST_STATE
	Residual for the last state vector. More...

DenseVector< _Type >	LAST_STATE
	The last state vector. More...

_Type	DELTA
	A default step for FD computation of the Jacobian. More...

unsigned	ORDER_OF_SYSTEM
	The order of the system of equations. More...

unsigned	NUMBER_OF_VARS
	The number of elements in the state vector. More...

Detailed Description

Define the Berman equation by inheriting Equation base class.

Define the Berman equation by inheriting the Equation base class.

Definition at line 24 of file BermanShooting.cpp.

Constructor & Destructor Documentation

◆ Berman_equation() [1/2]

CppNoddy::Example::Berman_equation::Berman_equation ( )

inline

Construct the Berman equation as a 4th order real system.

Definition at line 29 of file BermanShooting.cpp.

29: Equation<double> ( 4 ) {}

CppNoddy::Equation

An equation object base class used in the BVP/IVP classes.

Definition: Equation.h:22

◆ Berman_equation() [2/2]

CppNoddy::Example::Berman_equation::Berman_equation ( )

inline

The Berman equation is a 4th order real ODE.

Definition at line 27 of file BVPBerman.cpp.

27: Equation_1matrix<double>( 4 ) {}

CppNoddy::Equation_1matrix

An equation object base class used in the IBVP classes (and others).

Definition: Equation_1matrix.h:18

Member Function Documentation

◆ mass()

void CppNoddy::Example::Berman_equation::mass	(	const DenseVector< double > &	x,
		DenseMatrix< double > &	m
	)		const

inline

Definition at line 40 of file BermanShooting.cpp.

      {
        Utils_Fill::fill_identity(m);
      }

References Utils_Fill::fill_identity(), and m.

◆ matrix0()

void CppNoddy::Example::Berman_equation::matrix0	(	const DenseVector< double > &	x,
		DenseMatrix< double > &	m
	)		const

inlinevirtual

Define the matrix in terms of the current state vector.

Parameters

x	The current state vector.
m	The matrix.

Reimplemented from CppNoddy::Equation_1matrix< double >.

Definition at line 38 of file BVPBerman.cpp.

      {
        Utils_Fill::fill_identity(m);
      }

References Utils_Fill::fill_identity(), and m.

◆ residual_fn() [1/2]

void CppNoddy::Example::Berman_equation::residual_fn	(	const DenseVector< double > &	z,
		DenseVector< double > &	f
	)		const

inline

We implement the equation as 4 first-order ODEs.

Definition at line 32 of file BermanShooting.cpp.

      {
        f[ 0 ] = z[ 1 ];
        f[ 1 ] = z[ 2 ];
        f[ 2 ] = Re * ( - z[ 3 ] - z[ 1 ] * z[ 1 ] + z[ 0 ] * z[ 2 ] );
        f[ 3 ] = 0.0;
      }

References f, Re, and CppNoddy::Example::z().

◆ residual_fn() [2/2]

void CppNoddy::Example::Berman_equation::residual_fn	(	const DenseVector< double > &	z,
		DenseVector< double > &	g
	)		const

inline

The Berman equation.

Definition at line 30 of file BVPBerman.cpp.

      {
        g[ f ] = z[ fd ];
        g[ fd ] = z[ fdd ];
        g[ fdd ] = z[ fddd ];
        g[ fddd ] = Re * ( z[ f ] * z[ fddd ] - z[ fd ] * z[ fdd ] );
      }