Define the Falkner-Skan equation. More...

Inheritance diagram for CppNoddy::Example::FS_eqn:

Public Member Functions
	FS_eqn ()
	The FSE is a 3rd order ODE. More...

void	residual_fn (const DenseVector< double > &z, DenseVector< double > &f) const
	We implement the equation as 3 first-order real ODEs. 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 Attributes
double	beta
	The Hartree parameter. 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...

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 Falkner-Skan equation.

Definition at line 25 of file ArcShootFalknerSkan.cpp.

Constructor & Destructor Documentation

◆ FS_eqn()

CppNoddy::Example::FS_eqn::FS_eqn ( )

inline

The FSE is a 3rd order ODE.

Definition at line 29 of file ArcShootFalknerSkan.cpp.

29: Equation<double>( 3 ) {}

CppNoddy::Equation

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

Definition: Equation.h:22

Member Function Documentation

◆ residual_fn()

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

inline

We implement the equation as 3 first-order real ODEs.

Definition at line 32 of file ArcShootFalknerSkan.cpp.

      {
        f[ 0 ] = z[ 1 ];
        f[ 1 ] = z[ 2 ];
        f[ 2 ] = -z[ 0 ] * z[ 2 ] - beta * ( 1.0 - z[ 1 ] * z[ 1 ] );
      }

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

Member Data Documentation

◆ beta

double CppNoddy::Example::FS_eqn::beta

The Hartree parameter.

Definition at line 40 of file ArcShootFalknerSkan.cpp.

Referenced by residual_fn().

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

Tests/Arclength/ArcShootFalknerSkan.cpp

Public Member Functions

Public Attributes