Define the Lorenz equations by inheriting Equation base class. More...

Inheritance diagram for CppNoddy::Example::Lorenz_equations:

Public Member Functions
	Lorenz_equations ()
	Construct a 3rd order ODE. More...

void	residual_fn (const DenseVector< double > &z, DenseVector< double > &f) const
	We implement the equation as 3 first-order 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	a
	The usual 3 parameters of the Lorenz eqns. More...

double	b

double	c

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 Lorenz equations by inheriting Equation base class.

Definition at line 17 of file IVPLorenz.cpp.

Constructor & Destructor Documentation

◆ Lorenz_equations()

CppNoddy::Example::Lorenz_equations::Lorenz_equations ( )

inline

Construct a 3rd order ODE.

Definition at line 22 of file IVPLorenz.cpp.

22: 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::Lorenz_equations::residual_fn	(	const DenseVector< double > &	z,
		DenseVector< double > &	f
	)		const

inline

We implement the equation as 3 first-order ODEs.

Definition at line 25 of file IVPLorenz.cpp.

      {
        f[ 0 ] = a * ( z[ 1 ] - z[ 0 ] );
        f[ 1 ] = z[ 0 ] * ( b - z[ 2 ] ) - z[ 1 ];
        f[ 2 ] = -c * z[ 2 ] + z[ 0 ] * z[ 1 ];
      }